It can be solved via derivatives and intersections of curves. But how would you solve it in a purely algebraic manner using the W Lambert function?
In principle yes it can, the equation can be transformormrd to:
So formaly we have:
Now the problem is that there a multiple (real) branches of the Lambert W in
the region around , and you are going to have to
evaluate two of them to get all the solution to this. My LambertW calculator
gives .
However just plot the functions and you will see that there is another
solution near Numerical methods will find both solutions
once you know where they are.
RonL