I started with a rather complicated equation, and eventually managed to write it in the form $$ \left\{ \tanh \left(\frac{a\left(x-b\right)}{2}\right) - \tanh \left(\frac{ax}{2}\right) + 2 \log \left[ \frac{1+\tanh \left(\frac{a\left(x-b\right)}{2}\right)} {1+\tanh \left(\frac{ax}{2}\right)} \right] \right\} \times c + a\left(x-b\right) = d, $$ where $a$, $b$, $c$, and $d$ are constant parameters, and I would like to solve the equation for $x$. I tried the well-known trigonometric identities for the $\tanh\left(\cdot\right)$, but did not get any closer to obtain a closed-form solution for $x$. Do you have any suggestions on how to proceed, or whether there exists a closed-form solution to this problem?
Thank you in advance!