I seen a problem on another site where someone was wanting to know the inverse.
As Pka said, the derivative is always positive, so it has an inverse, but can not be found by elementary means.
I ran it through Maple and it kicked back:
What is Lambert?. I am unfamiliar. Does anyone know how this would be done without technology?. I thought it would something interesting to look into. I did find an interesting page on Wiki
In my engineering class we were studing a hanging cable. The problem is that the equations that describe it are hyperbolic functions and hence cannot be solved through "normally". However, I have been able to reduce the problem to solving,
In that case the linear-exponential equations can always be solved (I imagine). The full solution is here. http://www.mathhelpforum.com/math-he...e-problem.html