Question

When the difference between two numbers is equal to their xor

Answer 1

No.

If x=2n+1x=2n+1 and y=2ny=2n, then a=b=1a=b=1, but there is no way to determine nn.

It is easy to cook up more examples, if you arrange that you don't need to any "borrowing" (is that the correct English term?) when you do paper and pencil subtraction in base two. When that happens, subtraction gives the same result as XOR, but you cannot recover the positions of the cancelled bits.