  We calculate the contribution to the nuclear energy density functional which
arises from iterated pion-photon exchange between nucleons. In heavy nuclei,
this novel charge symmetry breaking interaction leads to an additional binding
of each proton by about 0.2 MeV. Compared to that the analogous effect from
irreducible pion-photon exchange is negligibly small. As a possible mechanism
to resolve the Nolen-Schiffer anomaly we propose the iteration of one-photon
exchange with an attractive short-range NN-interaction. The corresponding
energy per proton reads: $\bar E[\rho_p]=(2\alpha/15\pi^2)(\pi^2 -3+6 \ln2)
{\cal A}_{pp} k_p^2$ with $\rho_p =k_p^3/ 3\pi^2$ the proton density and ${\cal
A}_{pp}\approx 2 $fm an effective (in-medium) scattering length. Hints for such
a value of ${\cal A}_{pp}$ come from phenomenological Skyrme forces and from
the neutron matter equation of state.
