Novel methods to reconstruct the slant depth of the maximum of the longitudinal profile ( X max ) of high-energy showers initiated by gamma-rays as well as their energy ( E 0 ) are presented. The methods were developed for gamma rays with energies ranging from a few hundred GeV to ∼ 10 TeV. An estimator of X max is obtained, event-by-event, from its correlation with the distribution of the arrival time of the particles at the ground, or the signal at the ground for lower energies. An estimator of E 0 is obtained, event-by-event, using a parametrization that has as inputs the total measured energy at the ground, the amount of energy contained in a region near to the shower core and the estimated X max . Resolutions about 40 ( 20 ) g / cm 2 and about 30 ( 20 ) % for, respectively, X max and E 0 at 1 ( 10 ) TeV energies are obtained, considering vertical showers. The obtained results are auspicious and can lead to the opening of new physics avenues for large wide field-of-view gamma-ray observatories. The dependence of the resolutions with experimental conditions is discussed.