I couldn't resist chucking it into wolfram alpha https://www.wolframalpha.com/input/?i=solve+x^x+-+y+=+0 https://www.wolframalpha.com/input/?i=solve+x^x+-+y+=+0

I couldn't resist chucking it into wolfram alpha https://www.wolframalpha.com/input/?i=solve+x^x+-+y+=+0 https://www.wolframalpha.com/input/?i=solve+x^x+-+y+=+0 https://www.wolframalpha.com/input/?i=x%5Ex%3Dy https://www.wolframalpha.com/input/?i=x%5Ex%3Dy I think someone else mentioned W function, which is shown in the wolfram solution The thing I found interesting is the graph, there is a local min at 1/e, so the solution depends on y >1 or e^-1/e <= 1 very interesting curve.