  We present results on the pseudoscalar meson masses from a fully dynamical
simulation of QCD+QED. We concentrate particularly on violations of isospin
symmetry. We calculate the $\pi^+$-$\pi^0$ splitting and also look at other
isospin violating mass differences. We have presented results for these isospin
splittings in arXiv:1508.06401 [hep-lat]. In this paper we give more details of
the techniques employed, discussing in particular the question of how much of
the symmetry violation is due to QCD, arising from the different masses of the
$u$ and $d$ quarks, and how much is due to QED, arising from the different
charges of the quarks. This decomposition is not unique, it depends on the
renormalisation scheme and scale. We suggest a renormalisation scheme in which
Dashen's theorem for neutral mesons holds, so that the electromagnetic
self-energies of the neutral mesons are zero, and discuss how the self-energies
change when we transform to a scheme such as $\bar{MS}$, in which Dashen's
theorem for neutral mesons is violated.
