Solving Equations With Exponential Functions Involved

Hi everybody, this is my first post to mymathforum,

I have the following equation:

Is it possible to solve it for "t" ?

I tried with Mathematica and it told me that cannot be solved algebraically, but it can resolve it numerically with "FindRoot". However I need the analytical expression. I also tried to solve it by using the infinite series definition of the exponential function and the limit definition, both without success. Can anybody give more insights to solve it?

Thank you very much !