[Python shell, size 15, xnor](http://codegolf.stackexchange.com/a/41531/29611)
===
 1215954^1548696

Obtained by brute force in 1.42 seconds.

Code used to find solution:
<!-- language: lang-c++ -->

	#include <iostream>
	#include <algorithm>

	int main(){
		int digits[] = {1,1,1,2,4,4,5,5,5,6,6,8,9,9};
		int ndigits = sizeof(digits)/sizeof(digits[0]);
		
		do{
			int n1 = 0, n2 = 0;
			for(int i = 0; i < ndigits - 1; ++i){
				n1 = (n1 * 10) + digits[i];
				n2 = 0;
				for(int j = i+1; j < ndigits; ++j)
					n2 = (n2 * 10) + digits[j];
				if((n1 ^ n2) == 339018){
					std::cout << n1 << ' ' << n2 << std::endl;
					return 0;
				}
			}
		}while(std::next_permutation(&digits[0], &digits[ndigits]));
	}