How solve this optimization problem using cvx solve?

You have ti provide explicit formulas for E and T. Otherwise, no one on this forum will be able to help you.

F needs to be jointly convex in its argument. Otherwise, CVX can not be used for this problem. it is incumbent on you to prove (show) that tit is jointly convex in its arguments. That is addressed in the previously provided link, Why isn't CVX accepting my model? READ THIS FIRST! .