What is the most efficient way to solve an equation \begin{align*} (A\,E^{-1}\,C) x = b, \qquad A\in \mathbb{R}^{m\times n}, \, E \in \mathbb{R}^{n\times n}, \, C\in \mathbb{R}^{n\times m} \end{align*} for given vector $b \in \mathbb{R}^{m}$? The matrices $A,E,C$ are assumed to be sparse, and $A,C^T$ are not square, but both have full row-rank. Particularly, forming the inverse of $E$ explicitly should be avoided.
