Probably not.

[tex]= \frac{e^xe^{-y}- e^{-x}e^y}{e^xe^{-y}+ e^{-x}e^y}[tex]

I don't see any good way to separate the "x" and "y" terms and if you could you would still be left with y both in the exponential and linear so you would probably Lambert's W function to solvethat.