We report on a measurement of the cosmic ray energy spectrum by the Telescope Array Low-Energy Extension (TALE) air fluorescence detector (FD). The TALE air FD is also sensitive to the Cherenkov light produced by shower particles. Low-energy cosmic rays, in the PeV energy range, are detectable by TALE as Cherenkov events. Using these events, we measure the energy spectrum from a low energy of ̃2 PeV to an energy greater than 100 PeV. Above 100 PeV, TALE can detect cosmic rays using air fluorescence. This allows for the extension of the measurement to energies greater than a few EeV. In this paper, we describe the detector, explain the technique, and present results from a measurement of the spectrum using ̃1000 hr of observation. The observed spectrum shows a clear steepening near 10^17.1 eV, along with an ankle-like structure at 10^16.2 eV. These features present important constraints on the origin of galactic cosmic rays and on propagation models. The feature at 10^17.1 eV may also mark the end of the galactic cosmic ray flux and the start of the transition to extragalactic sources....