solve the SDE $dX_t=-\frac{1}{2}\exp\{-2X_t\}dt+\exp\{-X_t\}dW_t$

Question

where $t\in\mathbb{R_+}, X_0=a\in\mathbb{R}$ and $W=\{W_t\}_{t\ge0}$ is the standard Brownian motion.

I've tried exact SDE, linear SDE, and integrating factors but all failed.