An analytical approach to the problem of a negatively charged donor in an infinitely deep quantum well (QW) in the presence of parallel electric and strong magnetic external fields both directed perpendicular to the heteroplanes is developed. The double adiabatic approximation is employed. The dependences of the binding energy on the field strengths, the width of the well and the position of the impurity within the well are derived in explicit form. The effect of the inversion of the electric field is investigated. It is shown that the combined potential acting on the 'outer' electron resembles that of a double QW. When the levels associated with the two effective QWs anticross, a resonant structure arises. The explicit dependence of the resonant splitting on the width of the QW, the strength of the electric field and the position of the impurity are obtained. Using the parameters associated with the GaAs QW, estimates of the inversion shift of the binding energy and the frequency of the emitted resonant radiation induced by the electric field are made.