Analytic solution for $x = \frac{n}{1 + e^{-ax + t}}$ i.e. When is the output of a parametrised logistic function equal to the input?

Question

I would like to know when is the input to a parametrised logistic function (the right hand side) equal to its output.

I've been trying to solve the following equation:

$$x = \frac{n}{1 + e^{-ax + t}}$$

Is it possible to solve this equation analytically?

Thank you for any answers or ideas!