I wonder what the formal way to write "$f(x,y)=z$ can be solved for $x$"?
Maybe something like this:
Let $f\colon X\times Y\to Z, f(x,y)=z$ be such that there exists $g\colon Y\times Z\to X, g(y,z)=x$.
However, I feel that this hides the "solved for" part.