  We report the measurement of the helicity asymmetry $E$ for the $p\pi^0$ and
$n\pi^+$ final states using, for the first time, an elliptically polarized
photon beam in combination with a longitudinally polarized target at the
Crystal Ball experiment at MAMI. The results agree very well with data that
were taken with a circularly polarized photon beam, showing that it is possible
to simultaneously measure polarization observables that require linearly
(e.g.~$G$) and circularly polarized photons (e.g.~$E$) and a longitudinally
polarized target. The new data cover a photon energy range 270 - 1400 MeV for
the $p\pi^0$ final state (230 - 842 MeV for the $n\pi^+$ final state) and the
full range of pion polar angles, $\theta$, providing the most precise
measurement of the observable $E$. A moment analysis gives a clear observation
of the $p\eta$ cusp in the $p\pi^0$ final state.
