/ AbstractLOPES is a digital radio interferometer located at Karlsruhe Institute of Technology (KIT), Germany, which measures radio emission from extensive air showers at MHz frequencies in coincidence with KASCADE-Grande. In this article, we explore a method (slope method) which leverages the slope of the measured radio lateral distribution to reconstruct crucial attributes of primary cosmic rays. First, we present an investigation of the method on the basis of pure simulations. Second, we directly apply the slope method to LOPES measurements. Applying the slope method to simulations, we obtain uncertainties on the reconstruction of energy and depth of shower maximum Xmax of 13% and 50 g/cm^2, respectively. Applying it to LOPES measurements, we are able to reconstruct energy and Xmax of individual events with upper limits on the precision of 20-25% for the primary energy and 95 g/cm^2 for Xmax, despite strong human-made noise at the LOPES site.