Converting $x^y-y^x=1$ Into $y=$ Form

Question

This is probably going to be a simple answer, but, how would you convert $x^y-y^x=1$ into $y=$ form without any $y$ on the opposite side of the equation?

Answer 1

$x^y-y^x=0$ has a general solution in terms of the Lambert W function. $x^y-y^x=a\neq0,$ however, has no such general solution. If you wish, you may write ${\color{red}y}=\sqrt[\Large x]{x^{\color{red}y}-a}$ , and then repeatedly iterate the expression with regard to y.