One possible version:
Dear Ms. Smith,
I’m Li Hua, the leader of the Student Union of Yu Cai Middle School Middle School. I sincerely hope you can set aside some time for our English speech contest and be a judge.
The contest, the theme of which is “Man and Nature”, will be held in the Room 501 from 2:00 to 5:00 on the afternoon of June 15. What’s more, there will be 10 students taking part in it. I’m sure it will be a great success if you can give us some precious remarks. I would appreciate it if you could accept my invitation. My telephone number is 44876655.
I’m looking forward to your reply.
With best wishes,
Li Hua