I'm given the following system \$H\$ $$y(t)=\exp\left(-\intop_{-\infty}^{\infty}x(\tau)\cdot e^{-|t-\tau|}d\tau\right)$$ I proved it's TI (time-invariant) and that it's not linear.
Now we take as input \$y(t)\$ and we pass it through \$H_2\$, we are asked to construct \$H_2\$ such that the combination of \$H\$ and \$H_2\$ will be an LTI system.
When passing a linear combination of x signals through \$H\$ I get the following:
$$\exp\left(-{\displaystyle \intop_{-\infty}^{\infty}}ax_{1}\left(\tau\right)e^{-\left|t-\tau\right|}\right)\cdot\exp\left(-{\displaystyle \intop_{-\infty}^{\infty}}bx_{2}\left(\tau\right)e^{-\left|t-\tau\right|}d\tau\right)$$
In comparison to passing each part of it through \$H\$ and then multiplying each by the coefficients and adding them together
$$a\cdot\exp\left(-{\displaystyle \intop_{-\infty}^{\infty}}x_{1}\left(\tau\right)e^{-\left|t-\tau\right|}d\tau\right)+b\exp\left(-{\displaystyle \intop_{-\infty}^{\infty}}x_{2}\left(\tau\right)e^{-\left|t-\tau\right|}d\tau\right)$$
And this is where I'm stuck, I don't know how to get from all this information (from the question and my calculations) if a system \$H_2\$ is possible or not, and if it's possible I don't know how to derive it.
