In order to solve the problem of the excess of multi-muon events observed in several cosmic ray experiments at ultra-high energies (so-called ‘muon puzzle’), investigations of the energy characteristics of the muon component of extensive air showers (EAS) are required. A possible approach to such investigations is the measurement of the energy deposit of muon bundles in the detector, which provides information on the mean muon energy. In the experiment being now conducted at the NEVOD-DECOR complex, the local muon density and EAS arrival direction are determined according to the data of the coordinate-tracking detector DECOR, whereas the energy deposit is measured by means of the Cherenkov water calorimeter NEWOD. Simultaneous detection of muon bundles in a wide range of zenith angles and muon multiplicities ensures exploration of primary particle energy region of 10^16 – 10^18 eV and even higher. Results of the measurements of the energy deposit of the inclined muon bundles at various zenith angles based on the data accumulated during more than 29,000 h observations over the period from May 2012 to February 2017 are presented and compared with simulations performed by means of the CORSIKA program.