A set of kinetic differential equations relevant to the bleaching and excitation of thermoluminescence for the case of a single trapping state for electrons and a single variety of hole-recombination centre has recently been described and solved numerically. An approximate analytical solution to these equations is presented and the result compared with numerical solutions; good agreement between the analytical and numerical results is obtained. A simple analytical expression is given for the final equilibrium density of electrons at e-traps and the occupation number density of holes at r-centres, in terms of the initial densities of these carriers, and the recombination and trapping probabilities. These equilibrium values are found to be the same for both types of carrier. Furthermore, these equilibrium values do not have a very strong dependence on the incident irradiation intensity. The analysis also allows one, by a simple extension, to account for the wavelength dependence of the incident radiation. Other results that cannot be easily formulated with a purely numerical approach are also obtained. For instance, the conditions under which increases (excitation) and decreases (bleaching) in the electron density occur are given.