We analyze the high-energy Raman modes, G+ and G-, in a pair of one metallic and one semiconducting nanotubes. By combining Rayleigh scattering with Raman resonance profiles of the radial breathing mode and the high-energy modes, we show that the observed G- and G+ peaks can originate from longitudinal optical phonons of different tubes. The G- peak is the longitudinal mode of the metallic tube; it is broadened and downshifted due to strong electron-phonon coupling in the metallic nanotube. The G+ peak is due to the longitudinal mode in the semiconducting tube. This result resolves an ongoing debate in the literature.