  The current methods to determine the primary energy of ultra-high energy
cosmic rays (UHECRs) are different when dealing with hadron or photon
primaries. The current experiments combine two different techniques, an array
of surface detectors and fluorescence telescopes. The latter allow an almost
calorimetric measurement of the primary energy. Thus, hadron-initiated showers
detected by both type of detectors are used to calibrate the energy estimator
from the surface array (usually the interpolated signal at a certain distance
from the shower core S(r0)) with the primary energy. On the other hand, this
calibration is not feasible when searching for photon primaries since no high
energy photon has been unambiguously detected so far. Therefore, pure Monte
Carlo parametrizations are used instead.
  In this work, we present a new method to determine the primary energy of
hadron-induced showers in a hybrid experiment based on a technique previously
developed for photon primaries. It consists on a set of calibration curves that
relate the surface energy estimator, S(r0), and the depth of maximum
development of the shower, Xmax, obtained from the fluorescence telescopes.
Then, the primary energy can be determined from pure surface information since
S(r0) and the zenith angle of the incoming shower are only needed. Considering
a mixed sample of ultra-high energy proton and iron primaries and taking into
account the reconstruction uncertainties and shower to shower fluctuations, we
demonstrate that the primary energy may be determined with a systematic
uncertainty below 1% and resolution around 16% in the energy range from
10^{18.5} to 10^{19.6} eV. Several array geometries, the shape of the energy
error distributions and the uncertainties due to the unknown composition of the
primary flux have been analyzed as well.
