Block Diagram Reduction
My approach for solving the problem is as follows:

1.) Redraw the circuit with the goal not having any cross-couplings. That means: We have only simple feedback loops. 

2.) Therefore: Shift the input node for E to the right (after the summing junction). As a consequence the function of this block now must be (E+D)  

3.) Shift the input of B to the left (before the summing junction). Now, this block must have the function (B-D) instead of B only.  

4.) Now we have one simple forward path (E+D) in parallel to C resulting in (C+D+E) and two simple negative feedback loops which can be solved separately (Blacks formula).