Explainability Engineering gets evermore important in the era of self-learning and automated systems. We motivate the necessity for interdisciplinary research to engineer verifiably correct and good explanations: Systems engineering research must ensure that correct and machine-understandable explanations can be derived from system specifications and social sciences research must ensure that a context-dependent and stakeholder-tailored explanation can be provided in a fitting manner. We describe our first steps in the direction of a holistic and interdisciplinary explainability engineering process for tackling these challenges.