I've been trying to solve a Discrete LTI System problem where the overall impulse response of the following System, whose input and output sequences are, respectively, $x(n)$ and $y(n)$, has to be found:
This is what I've tried:
Calling the output sequence that comes out of the adder $e(n)$, I know that $y(n) = e(n) \star h(n)$. I also know that $e(n) = x(n) - y(n)$, which leads to $y(n) = x(n) \star h(n) - y(n) \star h(n)$. Thats the point where I got stuck. I don't know how to proceed in order to isolate $y(n)$ in the last expression. I would like to isolate it in order to make $x(n) = \delta(n)$ and evaluate the overall Impulse Response.
Also, I am not supposed to use any transform techniques as the book I am following has not yet arrived at those subjects. If possible, don't show the final calculations, only what I should do in order to separate $y(n)$. I would like to figure the rest out by myself.
Thanks in advance.