Pithy

Pithy..

(of language or style) concise and forcefully expressive.

synonyms:

succinct, terse, concise, compact, short (and sweet), brief, condensed,to the point, epigrammatic, crisp, thumbnail;

To the point.
Clear, forceful.

May your apologies be pithy and your explanations even pithier.

Your friend doesn't want to hear an "explanation" aka justification of your actions.
They want to know, that you listened to them.
That if you could do it again you would do it differently.
That you understand you hurt them, broke their trust, and can't just glue your relationship back together.

That you understand it will take time and patience and perseverance to rebuild what was broken between you.
And as always,

                            this is easier said than done.

But nothing worthwhile comes easy eh?