Comment by youareawesome

This is easily solved using the Lambert W function:

Observe: W(x * e ^ x) = x

    x ^ x = y
    ln(x ^ x) = ln(y)
    ln(x) * x = ln(y)
    ln(x) * e ^ ln(x) = ln(y)
    W(ln(x) * e ^ ln(x)) = W(ln(y))
    ln(x) = W(ln(y))
    x = e^W(ln(y))

https://en.wikipedia.org/wiki/Lambert_W_function