Im trying to solve this equation with respect to $m$ which is a $K×1$ vector:
$$\boldsymbol{\Sigma}^{-1}\boldsymbol{m}+\boldsymbol{W}^{T}\frac{\boldsymbol{1}-\exp(\boldsymbol{Wm}+\boldsymbol{W_0})}{\boldsymbol{1}+\exp(\boldsymbol{Wm}+\boldsymbol{W_0})}=\boldsymbol{W}^{T}(\boldsymbol{y}-\textbf{1/2})$$
where $\boldsymbol{\Sigma}$ is a $K×K$ matrix, $\textbf{W}$ a $D×K$ matrix, $\textbf{W}_0$ $D×1$ vector and $\textbf{y}$ a $K×1$ vector.
How can I handle the denominator in the fraction? Is there any general methodology for equations of this type?