I'd like to apply for a paid vacation from/kloc-0 to 10.
I will give all my work to ... with your consent.
Please let me know your opinion.
Yours, sincerely
XXX
Annual leave is also acceptable.
Supplementary answer:
Please approve that I want to take annual leave from1October 9-10. Thank you.
The grammar is a bit strange, but I can understand it. The suggestions are as follows:
Can you approve my annual leave on1October 9-10? Thank you.