Answer
${\rm \color{black}{\bf -10}\; nC,\; and\;\; \color{black}{\bf +40}\; nC}$
Work Step by Step
We have two charges $q_1$ and $q_2$and we know that the net electric potential energy is -180 $\mu$J.
Hence,
$$U=\dfrac{1}{4\pi \epsilon_0}\dfrac{q_1q_2}{r}$$
Hence,
$$q_1q_2=4\pi \epsilon_0 r U\tag 1$$
We are given that the net charge of both of them is about 30 nC, so
$$q_1+q_2=30\;\rm nC=30\times 10^{-9}\;C\tag 2$$
Hence,
$$q_1=(30\times 10^{-9})-q_2$$
Plug into (1),
$$ [(30\times 10^{-9})-q_2]q_2=4\pi \epsilon_0 r U$$
Plug the known;
$$ (30\times 10^{-9})q_2-q_2^2=\dfrac{1}{9\times 10^9} (2\times 10^{-2})(-180\times 10^{-6})$$
Hence,
$q_2= \bf -10\;\rm nC$ or, $q_2=40\;\rm C$
Plug into (2),
$q_1= \bf 40\;\rm nC$ or, $q_1=-10\;\rm C$
Therefore, the two charges are
$$\boxed{\rm \color{red}{\bf -10}\; nC,\; and\;\; \color{red}{\bf +40}\; nC}$$