Advice please?

Well, I have been smoking for a while now and today my parents found out.
My Dad was okay about obviously he wasn't happy but yeah, he was as good as can be expected.
My mum though, she went mad and started crying.
She said that I deliberately made her out to be a fool and that I have been laughing at her behind her back for months.
I haven't.
I feel so bad and now they probably don't trust me at all.
I want to tell my mum exactly how I felt about it and why I didn't tell her but I know that if I tlk to her it will only result in an argument of monumental proportions.
And this is where your advice becomes helpful.

I thought about writing her a letter to tell her exactly how I feel without the hassel of having to get into an argument.
Has anyone else been in this situation?
If so I would really like some advice on what to do because I am really at a loss at the moment.
Thanks in advance.
Charles.
xoxo