In the equation $x^x=y^y$, how do you solve for $y$ in terms of $x$ when $y$ is not $x$?

There is a small curve in the first quadrant which is not $y=x$. graph: https://www.desmos.com/calculator/l1jempmhhg


closed as off-topic by Leucippus, Alexander Gruber Apr 29 at 23:09

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    $\begingroup$ It doesn't look easy $\endgroup$ – Dr. Mathva Apr 29 at 21:09