Relative emission spectra of light-emitting diodes (LEDs) depend on the junction temperature. The high-energy region of the emission spectrum can be modelled with Maxwell-Boltzmann distribution as a function of energy and junction temperature. We show that according to the model and our experiments, the normalized emission spectra at different junction temperatures intersect at a unique energy value. The invariant intersection energy exists for many types of LEDs and can be used to determine the alloy composition of the material. Furthermore, the wavelength determined by the intersection energy can be used as a temperature invariant wavelength reference in spectral measurements.