  Since its commissioning in autumn 2012, Tunka-Rex, the radio extension of the
air-Cherenkov detector Tunka-133, performed three years of air shower
measurements. Currently the detector consists of 44 antennas connected to
air-Cherenkov and scintillator detectors, respectively, placed in the Tunka
valley, Siberia. Triggered by these detectors, Tunka-Rex measures the radio
signal up to EeV-scale air-showers. This configuration provides a unique
possibility for cross-calibration between air-Cherenkov, radio and particle
techniques. We present reconstruction methods for the energy and the shower
maximum developed with CoREAS simulations, which allow for a precision
competitive with the air-Cherenkov technique. We apply these methods to data
acquired by Tunka-Rex in the first year which we use for cross-calibration, and
we compare the results with the reconstruction of the energy and the shower
maximum by Tunka-133, which provides also a reconstruction for the shower core
used for the radio reconstruction. Our methods have shown that the atmospheric
depth of the shower maximum ($X_\mathrm{max}$) can be reconstructed with a
precision of better than 40 g/cm$^2$ for high quality events, in some cases
even when only three antenna stations have signal. The energy precision is
comparable with the air-Cherenkov precision of 15%. Soon the results will be
checked with the independent data of the second year.
