  The linear term proportional to $|N-Z|$ in the nuclear symmetry energy
(Wigner energy)is obtained in a model that uses isovector pairing on single
particle levels from a deformed potential combined with a $\vec T^2$
interaction. The pairing correlations are calculated by numerical
diagonalization of the pairing Hamiltonian acting on the six or seven levels
nearest the $N=Z$ Fermi surface. The experimental binding energies of nuclei
with $N\approx Z$ are well reproduced. The Wigner energy emerges as a
consequence of restoring isospin symmetry. We have found the Wigner energy to
be insensitive to the presence of moderate isoscalar pair correlations.
