inverse problem about scalar multiplication on elliptic curve
As Samuel Neves described in the comments it is trivially possible to obtain $P$ from $Q=[n]P$, given $Q$ and the integer $n$.

Simply compute $k=n^{-1} \bmod \ell$, with $\ell=|E(\mathbb F_p)|$ being the order (= the number of points) of the curve. $\ell$ is usually known.

Then, to obtain the desired point $P$, calculate $P=[k]Q=[kn]P$ and you're done.