Answer
$E = 0$
Work Step by Step
We can draw a Gaussian sphere with radius $r$ with the same common center as the two spherical shells.
We can find the electric field at a distance $r$ from the common center:
$\epsilon_0~\Phi = q_{enc}$
$(\epsilon_0)~(E)(4\pi~r^2) = q_{enc}$
$E = \frac{q_{enc}}{4\pi~\epsilon_0~r^2}$
$E = \frac{0}{4\pi~\epsilon_0~r^2}$
$E = 0$
