Easiest way to find y in $x \text{ xor } y = z$ with given $x \text{ and } z$
One can observe that, for any boolean values $a,b,c$, we have 
$a=b$ if and only if 
$a \text{ xor } c = b \text{ xor } c$.

(To prove that we note that $\Rightarrow$ is trivial, and $\Leftarrow$ follows by xor-ing with $c$ once more and applying the cancellation law.)

Hence, the equation
$x \text{ xor } y = z$
is equivalent to
$(x \text{ xor } y) \text{ xor } x = z \text{ xor } x$
which in turn (by the cancellation law), simplifies to
$y = z \text{ xor } x$.

If we wanted to be more pedantic we could explicitly point out those steps where we also implicitly used associativity, commutativity, and the identity law.