  We present a reconstruction algorithm for extensive air showers with zenith
angles between 65$^\circ$ and 85$^\circ$ measured with radio antennas in the
30-80 MHz band. Our algorithm is based on a signal model derived from CoREAS
simulations which explicitly takes into account the asymmetries introduced by
the superposition of charge-excess and geomagnetic radiation as well as by
early-late effects. We exploit correlations among fit parameters to reduce the
dimensionality and thus ensure stability of the fit procedure. Our approach
reaches a reconstruction efficiency near 100% with an intrinsic resolution for
the reconstruction of the electromagnetic energy of well below 5\%. It can be
employed in upcoming large-scale radio detection arrays using the 30-80 MHz
band, in particular the AugerPrime Radio detector of the Pierre Auger
Observatory, and can likely be adapted to experiments such as GRAND operating
at higher frequencies.
