There is a certain function called the Lambert W-function defined as the inverse of the function . Here, we have so it follows that if we take the W-function of both sides,
This is pretty much the simplest form that one can express x in, even though the W-function is somewhat obscure. There is, of course, using Newton's method, but it is very unlikely that a real number will be obtained.
Also, I checked my answer on Wolfram Alpha by putting arbitrary values for A and B (e.g. A = 253, B = 19), and it came out with the solution .
