A new method to reconstruct the slant depth of the maximum of the longitudinal profile ($X_{\rm max}$) of high-energy showers initiated by gamma-rays as well as their energy ($E_0$) are presented. The method was developed for gamma rays with energies ranging from a few hundred GeV to around 10 TeV. An estimator of $X_{\rm max}$ is obtained, event-by-event, from its correlation with the distribution of the particles' arrival time 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 $X_{\rm max}$. Resolutions about 40 (20) g/cm2 and about 30(20)\% for, respectively, $X_{\rm max}$ 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.