I got a T10 admit last year. Should I mention that in my essays?

I would also advise against it for the reasons mentioned above, plus the fact that it might make you look flaky in the eyes of adcoms. Schools care about their yield rates, so telling them that you passed on starting school this fall even though you had a T10 admit in hand isn't going to look great, regardless of what personal reasons you may have had.

I'd strongly recommend that you don't as it doesn't solve any purpose but can only give a wrong impression about you.
If you are reapplying to b-schools, you will have to write an additional reapplicant essay. Besides your T10 admit not being relevant for the b-schools, the space offered for the reapplicant essay is usually very short (200 to 350 words). You should utilize that properly to write something about how your candidature has improved since you last applied. Adding about a previous admit will make you sound boastful for no reason.

Typically the best reapplicant essays (that will make your case stronger) are the ones that show:
1. growth in job profile and ECAs
2. more maturity
3. better understanding of the program where you are reapplying. Make them see how it fits into your career aspirations, how you will gain from the b-school, and more importantly, how will you contribute to others.
4. better understanding of goals if your goals were vague in the last application.

Hope that helps