These response-model equations are quite complicated and some involve a nonelementary integral; the exact solutions can be found here [REF].
L_{CW} = \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,T_{CW} \,\, = \,\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\hat Q_0 \,\, = \,\, .