A question: how to invert a boolean equation?

I have a (linear) equation, like: $x+123*y = 1000$. And I want to invert it. I want to know, what y would be depending on x. Using Wolfram Mathematica, I do:

Solve[x+123 y = 1000, y]

Output: y=(1000-x)/123

( Wolfram Alpha )

OK. Now what if I want to use boolean operations, such as XOR, AND, OR? Mathematica's Solve[] can't handle that.

For example: $x \oplus z + y = 10000$. I expect such an output: $z=x \oplus (10000-y)$

I want a general method of solving boolean equations for a specific variable, like:

input: x XOR z + y = 10000
output: z=x XOR (10000-y)

More operations/variables may be added...

Questions:

1) Of course, I can do this by hand (for small equations). But is there a math tool that can do it? Wolfram's, Maple, Matlab, Sage, etc?

2) Is it just rewriting anyway, what Mathematica's Solve[] does?


TIA! first(a)last.com