Bitwise Operators: Using only & and ~ to get ^

I've been stuck on a bonus my professor gave for a couple of days now:

• give x^y using only ~ and &
• Assume the machine use twos complement, 32-bit representations of integers.

I've tried many different combinations, and also tried to write out the logic of the operator ^, but it hasn't been working out. Any hints or help would be much appreciated!

The XOR operator can in fact be written as a combination of those two. I'll put this in two steps:

A NAND B = NOT(A AND B)

A XOR B = (A NAND (A NAND B)) NAND (B NAND (A NAND B))

As described before on math:

https://math.stackexchange.com/questions/38473/is-xor-a-combination-of-and-and-not-operators