This paper introduces the principle method and simulation of an asymmetric TE (transverse electric) mode absorption in a lossy artificial metamaterial (LHM (left-handed material)). LHM is sandwiched between a lossy substrate and covered by a lossless dielectric cladding. The asymmetry solutions of the eigenvalue equation describe lossy-guided modes with complex-valued propagation constants. The dispersion relations, normalized field and the longitudinal attenuation were numerically solved for a given set of parameters: frequency range; film's thicknesses; and TE mode order. We found that high order modes, which are guided in thinner films, generally have more loss of power than low-order modes since the mode attenuation along z-axis , the modes of order (4, 5, 6) attain high positive attenuation which means these modes have larger absorption lengths and they are better absorber than the others. This LHM is appropriate for solar cell applications. For arbitrary LHM, at frequency band of wavelengt (600, 700 to 900 nm), the best absorption is attained at longer wavelengths and for lower order modes at wider films. The obtained results could be useful for the design of future light absorbers.