Given the following recursion relation \begin{equation} E^{(n)}=(E^{(n-1)}-\alpha_1)\,e^{-\alpha_2\,(\alpha_3E^{(n-1)}+b)} \end{equation}
where $\alpha_i$'s and $b$ are some constants.
I am trying to find $E^{(n)}$ as a function of $E^{(1)}$, but I am not sure if there is a clear way to do so, what do you guys think?