Electric field within a sphere

1. The problem statement, all variables and given/known data
A sphere with radius r has uniform charge density ρ within its volume, except for a small hollow sphere located at the center with radius R. Find the electrical field.

2. Relevant equations
ρ=Q/V
∫∫EdS=Q/ε

3. The attempt at a solution
With the spherical Gaussian surface with radius r:
[itex] E4 \pi r^2=\dfrac{\rho \frac{4\pi r^3}{3}}{\epsilon} [/itex]

Is it just a case of finding the electric field from setting a Gaussian surface to the hollow sphere as well and subtracting?

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