Answer
See the detailed answer below.
Work Step by Step
The maximum energy stored in the capacitor, in $LC$ circuits, is equal to the maximum energy stored in the inductor since the energy in the circuit alternates between the inductor and the capacitor.
So
$$(U_L)_{\rm max}=\frac{1}{2}LI_{\rm max}^2 =(U_C )_{\rm max}$$
So,
$$L=\dfrac{2(U_C )_{\rm max}}{I_{\rm max}^2}$$
Plug the known;
$$L=\dfrac{2(1\times 10^{-5})}{(0.1)^2}$$
$$L=\color{red}{\bf 2.0}\;\rm mH$$
Recalling that
$$\omega=2\pi f=\dfrac{1}{\sqrt{LC}}$$
Hence,
$$C=\dfrac{1}{4\pi^2f^2L} $$
Plug the known;
$$C=\dfrac{1}{4\pi^2(10\times 10^3)^2(2\times 10^{-3})}$$
$$C=\color{red}{\bf 0.127}\;\rm \mu F $$
