Class-E amplifiers don't work in such a way...
They work always in switching mode so hard saturation mode, not linear or triode region etc...
For these kind of amplifiers, finding an input matching network is not easy task but a "rough approximated" circuit will serve,no problem.
Output L-C circuits are very important for efficiency,harmonic levels etc. Therefore there is no way out but a nonlinear simulator preferable HB...
If you intend to build up this amplifier with 2 stages, first stage can be A or AB class but only last stage will be E-class because E-Class amplifiers are "practically" used at output stages.