A technique used to recover lost packets consists on sending a recovery packet with the XOR of the bits from the previous packets.

Eg:
Packet A = 101
Packet B = 001
Recovery R = A XOR B = 010

If packet A is lost, it can be recovered with B XOR R = A.
If packet B is lost, it can be recovered with A XOR R = B.

Why does this work and what's the mathematical explanation behind it?