Hardness of problem related to bilinear pairings
What you present is a generalized version of the so called fixed-argument pairing inversion (FAPI) problem. The FAPI problem is given an element $z\in G_T$ and an element $h\in G$ to compute $f\in G$ such that $e(h,f)=z$. 

Note, that FAPI is implied by the computational Diffie Hellman problem: Given $(g,g^a,g^b)\in G^3$, call the FAPI oracle with $z\gets e(g^a,g^b)$ and $h\gets g$ and clearly we have that $f=g^{ab}$ which is a solution to the CDHP in $G$.

The generalized (GPI) version is that when given $z\in G_T$ to compute $h,f\in G$ such that $e(h,f)=z$. Obviously, GPI implies FAPI.

Pairing inversion is AFAIK generally believed to be hard. You may study this paper or this blog post for more details.