For the non-hyperfine interaction part:
E(J) = -g*mu_N*B0*m_J => delta E = E(-3/2) – E(-1/2) = -g*mu_N*B0(-3/2+1/2) = 1*1*5.788*10^-4 eV/T * 2T = 0.12 meV.

For the hyperfine interaction part:
E(J) = -g*mu_N*B0*m_J + A*mI*mJ = -g*mu_N*B0*m_J + (g*mu_N*B_hf)/J * mI*mJ

for mJ=-3/2 and -1/2:
delta E = 0.12 meV + mI*mJ*g*mu_N*B_hf(-2/3 + 6/3) = 0.12 * 10^-3 + (3/4)*1*5.788*10^-4 eV/T * 10 T * (-4/3) = 0.12 * 10^-3 eV + 5.8 * 10^-3 eV = 5.8 meV

for mJ=-1/2 and -1/2:
delta E = E(-1/2) – E(1/2) = 0 + (1/4)*g*mu_N*B_hf * 4 = 1*5.788*10^-4 eV/T*10T = 5.7 meV