I really cannot understand how to derive the transfer function from the attached block diagram. It especially confuses me around the E-B-E loop.
It helps if you label some internal states. For example lets call the signal coming out of block $A$ $x_1$ and the signal coming out of block $B$ $x_2$. From the block diagram it follows that,
$$ A\, (U - D\, x_2) = x_1, $$
$$ B\, (x_1 - E\, x_2) = x_2, $$
$$ Y = E\, x_2 - C\, x_1. $$
Assuming $U$ is known, than you have three linear equations and unknowns ($x_1$, $x_2$ and $Y$), which should be solvable.