"An apology is good."
Schuld is the root word, it means guilt/blame/fault. Schuldig means guilty. Ent- is a prefix that means something like un-. (Entdecken means uncover/discover, die Decke is blanket.) -ung makes adjectives into nouns.
It is all right if you know how to apologise. There the tone will be important, not the spelling.
Well, if you really want to make peace with him, "an apology is (would be) good";
It's eine because it is feminine. You can tell it's feminine because of the 'ung' ending. It would be "ein" if it was masculine or neuter.