As far as I know, Y(X) cannot be expressed in elementary functions in general.
so the equation can be written as or . Let Z= -Yln(X). Then and so the equation becomes and then .
Now apply "Lambert's W function" to both sides. "Lambert's W function" is defined as the inverse function to so . Of course, "Lambert's W function" is NOT an "elementary function" so emakarov is completely correct.