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C, 57 5350 40 bytes

The rules are somewhat confusing, I do hope I read them correctly.
Works on 32bit platforms only.

m="E=mc^2"; main(c){ c=-1u/2; puts(m*c*c); } 

cc equals 2^31-1, so c*c equals 1 modulo 2^32. Therefore m*c*c == m (mod 2^32).
The -1u/2 constant and puts are hvd's suggestions.

C, 57 53  50 40 39 bytes

The rules are somewhat confusing, I do hope I read them correctly.
Works on 32bit platforms only.

m="E=mc^2",c=-1u/2; main(){ puts(m*c*c); } 

cc equals 2^31-1, so c*c equals 1 modulo 2^32. Therefore m*c*c == m (mod 2^32).
The -1u/2 constant and puts are hvd's suggestions.

C, 57 53 50 bytes

The rules are somewhat confusing, I do hope I read them correctly.

m="E=mc^2"; main(c){ m/=4; c=2; printf("%s\n",m*c*c); } 

Only works on 32bit platforms.

Assumes the address of s is a multiple of 4, which is quite likely to be true. The following program is more robust, but longer (58 bytes). It works because 954437177*9 is 1 modulo 2^32.

m="E=mc^2"; main(c){ m*=954437177; c=3; printf("%s\n",m*c*c); } 

C, 57 5350 40 bytes

The rules are somewhat confusing, I do hope I read them correctly.
Works on 32bit platforms only.

m="E=mc^2"; main(c){ c=-1u/2; puts(m*c*c); } 

cc equals 2^31-1, so c*c equals 1 modulo 2^32. Therefore m*c*c == m (mod 2^32).
The -1u/2 constant and puts are hvd's suggestions.

C, 57 53 bytes

The rules are somewhat confusing, I do hope I read them correctly.

s="E=mc^2",m; main(c){ m=s/4; c=2; printf("%s\n",m*c*c); } 

Only works on 32bit platforms.
Assumes the address of s is a multiple of 4, which is quite likely to be true (this can be fixed for 7 bytes, using m=s;c=2147483647;).

C, 57 53 50 bytes

The rules are somewhat confusing, I do hope I read them correctly.

m="E=mc^2"; main(c){ m/=4; c=2; printf("%s\n",m*c*c); } 

Only works on 32bit platforms.

Assumes the address of s is a multiple of 4, which is quite likely to be true. The following program is more robust, but longer (58 bytes). It works because 954437177*9 is 1 modulo 2^32.

m="E=mc^2"; main(c){ m*=954437177; c=3; printf("%s\n",m*c*c); }