  Starting in summer 2021, the Radio Neutrino Observatory in Greenland (RNO-G)
will search for astrophysical neutrinos at energies >10 PeV by detecting the
radio emission from particle showers in the ice around Summit Station,
Greenland. We present an extensive simulation study that shows how RNO-G will
be able to measure the energy of such particle cascades, which will in turn be
used to estimate the energy of the incoming neutrino that caused them. The
location of the neutrino interaction is determined using the differences in
arrival times between channels and the electric field of the radio signal is
reconstructed using a novel approach based on Information Field Theory. Based
on these properties, the shower energy can be estimated. We show that this
method can achieve an uncertainty of 13% on the logarithm of the shower energy
after modest quality cuts and estimate how this can constrain the energy of the
neutrino. The method presented in this paper is applicable to all similar radio
neutrino detectors, such as the proposed radio array of IceCube-Gen2.
