I actually posted a reply to this above, knowing both the sum and the xor is not sufficient to determine the two variables. Consider a situation where you know

I actually posted a reply to this above, knowing both the sum and the xor is not sufficient to determine the two variables. Consider a situation where you know that (a xor b) = 1 and (a - b) = 1. Both a missing 2/extra 3 and missing 4/extra5 and any 2^N/2^N+1 are solutions to that equation. Just because you have two equations and two unknowns doesn't necessarily mean you end up with a single value for each except in certain circumstances (eg they are linear equations of full rank).