Indem and dadurch, dass are used in adverbial clauses of manner. These conjunctions express manner/method/way of doing something.
I hear a borrowed English word ‘sorry’ more often than any of its German equivalents. Somehow Germans like this word. The online Duden dictionary gives the definition of the word as: ‘freundschaftliche Höflichkeitsformel zur Entschuldigung’ and notices that German ‘sorry’ comes from English ‘sorry’ (who would have doubt about that?!). Duden dictionary remarks that ‘sorry’ belongs to colloquial speech. It is such a relief to know that! For some reasons, I feel that Germans do not treat ‘sorry’ the same way as native English speakers do.