The scope of what I'm looking at is much broader, but I've simplified it down to this form:
Where A/A1 and B/B1 are known initial conditions, and C1/C2 are constants to solve for, I have these equations to solve simultaneously. The other forms I work with I fit into matrices to solve no problem, and I'm looking at the best way to solve this form.
A + C1 + (A XOR C2) = A1
B + C1 + (B XOR C2) = B1
Please note that these all represent real integers, in range 0 - 0xFFFF.
A practical real example is below (example only, not necessarily solveable):
0x32A3 + C1 + (0x32A3 XOR C2) = 0xF82B
0x873C + C1 + (0x873C XOR C2) = 0xD18A
Most troubling for me is if its possible to algebraically solve the bitwise XOR operation like this. Is there a NON-substitution approach to take?