  We study the Okamoto-Nolen-Schiffer (ONS) anomaly in the binding energy of
mirror nuclei at high density by adding a single neutron or proton to a quark
gluon plasma. In this high-density limit we find an anomaly equal to two-thirds
of the Coulomb exchange energy of a proton. This effect is dominated by quark
electromagnetic interactions---rather than by the up-down quark mass
difference. At normal density we calculate the Coulomb energy of neutron matter
using a string-flip quark model. We find a nonzero Coulomb energy because of
the neutron's charged constituents. This effect could make a significant
contribution to the ONS anomaly.
