We can express the solution in terms of the Lambert-W function, the inverse of f(x) = x*exp(x). We still need a new function, but at least Lambert-W comes up i

We can express the solution in terms of the Lambert-W function, the inverse of f(x) = x*exp(x). We still need a new function, but at least Lambert-W comes up in other places as well- not much worse than introducing log.