Java - 44 bytes

int n(int a,int b){return Math.abs(a+(-b));} 

Returns an absolute value of a + (-b)

Ungolfed version:

int n(int a, int b) { return Math.abs(a + (-b)); } 

ForceLang, 33 bytes

def a io.readnum() io.write a+a+1 

Cardinal, 7 bytes

%:+~:*. 

Outputs sum + 1

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Melang (Non competing) 13 bytes

\n\n+\n+\n\ni 

I wrote Melang for this challenge and decided that it works so might as well bring it here.

Adds the numbers inputted together and adds one. For more on the language and to try it out visit here.

Haskell, 11 9 bytes

(succ.).(+) 

Adds together and then adds 1

EDIT: Of course, if you want to go with the boring answer:

a#b=a+b+1 

is 9 bytes.

c++, 28 bytes

[](int a,int b){return!a+b;} 

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Japt, 3 bytes

NxÄ 

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Explanation

N :The array of all inputs x :Sum the array Ä :Add one to each element 

Aceto, 9 bytes

ir+1 ri+p 

Super straightforward. Prints the sum of the two inputs and 1. If I can assume for the inputs to be on the stack already, there's a 5-byte solution:

1+ +p 

MarioLANG, 35 bytes

; ) ; >[!(+: "=#=== ) - + ( ! < #=" 

Reads two inputs and puts them in differents cells (variables). Increments one and decrements the other until the second number is zero. Then adds one calculate the wrong answer.

Underload, 23 bytes

((::)~*)~(~)~*a*^*(**)* 

Takes input in the form of Church numerals on the stack and outputs to the stack.

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Excel VBA, 13 Bytes

Anonymous VBE immediate window function that takes input from range [A1:B1] (... or really any range that is a subset of [1:1], I suppose) and outputs their sum +7

?[Sum(1:1)+7] 

Windows batch, 24 23 17 bytes

@cmd/cset/a%1+%21 

Test cases:

Tested on Win10 64-bit

Foo\Bar\Baz>NotCalc.bat 1 55 552 

Note: batch files are limited to 32-bit signed integer!

Perl 5, 8 bytes

7 bytes of code + 1 flag (-p)

$_+=!<> 

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Aceto, 6 bytes

rrJiIp 

 r reads input and puts on stack (x2) J concatenates top 2 values i makes it an integer I increments it p prints it

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Implicit, 2 bytes

+. 

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+. implicit input of two integers + add them . and increment 

= also works for 1 byte, but I added that to the existing list of =s.

x86 opcode, 2 bytes

INC EDX RET 

input EAX and EDX, output EDX:EAX If D':A=D+A then D has to be zero, making the equation still not correct

x86 opcode __cdecl, 3 Bytes

MOV DL, 3 RET 

MAWP, 4 bytes

@MM: 

adds the numbers to the 1 in stack.

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Google Sheets, 9

=--(A1=A2 

• If A1=A2, the sum is even, but the output is always 1, which is odd.
• If A1<>A2, then the sum is positive, but the output is always 0, which is not positive.

Why didn't I use =A1+A2+1? Because if I input a sufficiently large number and 0, the +1 does nothing.

HBL, 2 bytes

+.,1 

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Explanation

+ Add . the first argument , the second argument 1 and one 

Braingolf, 3 bytes

g1+ 

Appends the inputs to eachother (ie 17, 4 becomes 174), then increments by 1.

Notable testcases:

[0, 0] becomes 00, becomes 01 [0, 1] becomes 01, becomes 02 [1, 0] becomes 10, becomes 11 [1, 1] becomes 11, becomes 12 

Thunno 2, 1 byte

= 

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Port of @ATaco's RProgN answer.

Vyxal HṪ, 2 bytes

□∑ 

I had to post this as it is quite obfuscated.

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Explanation

□∑­⁡​‎‎⁡⁠⁡‏‏​⁡⁠⁡‌⁢​‎‎⁡⁠⁢‏‏​⁡⁠⁡‌­ □ # ‎⁡Get input treated as a list separated by newlines. ∑ # ‎⁢Sum the list together. 💎 Created with the help of Luminespire at https://vyxal.github.io/Luminespire 

With the explanation above, it seems like that this returns the correct sum. But if you think this, then you haven’t paid attention to the flags.

HṪ­⁡​‎‎⁡⁠⁡‏‏​⁡⁠⁡‌⁢​‎‎⁡⁠⁢‏‏​⁡⁠⁡‌­ H # ‎⁡Before execution, push 100 to the stack. Ṫ # ‎⁢After execution, take the sum of the whole stack and print it. 💎 Created with the help of Luminespire at https://vyxal.github.io/Luminespire 

Now that you have the full picture, you realise that it adds 100 to the result.

Acc!!, 31 bytes

Count i while N-10 { Write 57 } 

Takes the two numbers space-separated. Try it online!

Explanation

Count i while N-10 { # While input character is not a newline: Write 57 # Output 9 } 

To prove that the output is always valid, consider the following numbers:

• A + B = the sum of the input numbers
• AB = the concatenation of the input numbers (equal to A * 10 ^ (len B) + B)
• N = a number of the same length as AB but composed of all 9's
• N⁺ = N with an extra 9 concatenated (equal to N * 10 + 9)

The output of this program is N⁺ (the extra 9 comes from the space between the input numbers). Looking at the formulas, we have A + B <= AB, AB <= N, and N < N⁺; therefore, this program's output is always greater than (and therefore not equal to) A + B.

brainfuck, 18 bytes

,[>-[----->+<]>.,] 

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Output is always lot larger than input

Zsh, 8 bytes

<<<9$1$2 

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Concatenates 9 A B which is always larger than A + B

><>, 3 bytes

Also see this post, but ><> needs the explicit print and termination so we can't go under 3 bytes.

=n; 

But this is a pretty boring solution. There are two 5 byte solutions

1nnn; 

and

1++n; 

that are only slightly more interesting. For input a and b, the first one works by printing 1ba and the second by printing a+b+1.

Here is a TIO test bench where bytes 2-5 should be replaced by the first 4 bytes of a solution.

Setanta, 29 28 bytes

Thanks to General Grievance for −1 byte

gniomh(a,b){toradh a==b|0&1} 

Returns 1 if the arguments are equal; 0 otherwise.

try-setanta.ie link

Bespoke, 49 bytes

using C added a specific pair segfault o,stupid C 

Outputs !(A+B).

GolfScript, 3 bytes

Input is to be taken as two separate lines. In GolfScript, a preceding 0 is allowed for numbers.

n/0 

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Explanation

# Two inputs taken with newlines n/ # Split the input (separated by newlines) with newlines 0 # Add a 0 to prevent a preceding 0 # Implicit concatenation 

GolfScript, 3 bytes

~+) 

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Explanation

~ # Evaluate the input + # Add the two numbers ) # Increment the sum 

1+, 6 bytes

..+1+: 

As usual. a + b + 1.