System invertability
$$ y[n] = x[n-2] - 2 x[x-8] $$

that's actually a linear and time-invariant system.  you invert it by computing the Z transform

$$ Y(z) = z^{-2}X(z) - 2 z^{-8}X(z) $$

solve for $X(z)$, then inverse Z transform.  you might find out that, to invert this system, you will have to look at future samples, so the inverse would not be causal.