What to say to someone I hurt (emotionally)?

To make a long story short, my friend who I'll call Emma convinced me to tell a secret of I'll call him Grady's to our whole Discord and I gave in to the peer pressure.

I tried to explain to him over text that it wasn't my fault (that failed). He told me, "leave me alone"

Now, I sit with him and his friends at lunch (next to emma on the same side of the table as him, so i'm not in his line of sight)

Once the shock of me being there wears off, what would be the best way to start the apology conversation?