As part of an answer to a Stack Overflow question I made the assumption that if I choose two distinct positive integers $m$ and $n$, them give you $m - n$ and $m$ XOR $n$, then you can uniquely determine what $m$ and $n$ were. For all the examples I've tried this seems to work correctly, though I have no reason to believe that this should work in general. Moreover, I'm not familiar enough with the interactions of differences (or sums, for that matter) and XOR to deivse a proof or counterexample.
Is my claim true? If so, how would you go about proving it? If not, is there a nice counterexample?
Thanks so much!