Basically what we need to do is look at the perturbed energy. This can be described as a product of the magnetic moment and the magnetic field B(0) in case there is no hyperfine interaction. We can rewrite this expression as a product of the Bohr magneton, the Landé g-factor, the magnetic field and the Zeeman level m_j. Now it is just a piece of cake to compute the energy difference. For the difference m_j =-3/2 and m_j=1/2 we get 231 µeV and for +1/2, -1/2 we get 116 µeV.
If we allow for hyperfine interactions, then the we need to take into account an extra perturbation A m_J m_I, with A the hyperfine parameter µB_hf/ IJ. This is also easily calculated as g µ_N B_hf / J = 1 * 3.152 e-8 * 10 / (3/2) = 2.10 e-7. So the correction for 1/2 1/2 is 5.28e-8 and for 3/2 1/2 1.576 e-7