The Tunka-Radio extension (Tunka-Rex) is a radio detector for air showers in Siberia. From 2012 to 2014, Tunka-Rex operated exclusively together with its host experiment, the air-Cherenkov array Tunka-133, which provided trigger, data acquisition, and an independent air-shower reconstruction. It was shown that the air-shower energy can be reconstructed by Tunka-Rex with a precision of 15% for events with signal in at least 3 antennas, using the radio amplitude at a distance of 120 m from the shower axis as an energy estimator. Using the reconstruction from the host experiment Tunka-133 for the air-shower geometry (shower core and direction), the energy estimator can in principle already be obtained with measurements from a single antenna, close to the reference distance. We present a method for event selection and energy reconstruction, requiring only one antenna, and achieving a precision of about 20%. This method increases the effective detector area and lowers thresholds for zenith angle and energy, resulting in three times more events than in the standard reconstruction.