I am not a mathematician and I am not familiar to that type of equations, so I don't really have any idea. More context: This equation came up when I took the derivative of the log-likelihood function of a machine learning model and set it to 0. I need to solve this equation to get the update rule for $x$, which is a latent variable of the system. The reason why I have both $x$ and exponential of $x$ in this equation is because there are both Gaussian variables and Bernoulli variables in the machine learning model.
– user5054Sep 07 '17 at 07:32
2
In general, such equations can only be solved numerically using, for example, Newton's Method.
– Gerry MyersonSep 07 '17 at 07:45