Small correction to your maths but not your sentiment.

10^100 years - 10^14 years = approx. 10^100 years

In the same way that:

10^6 - 10^3 = 1,000,000 - 1000 = 999,000 which is more or less approx. 10^6

Edit: Although this is one of those relatively uncommon situations where it doesn't really matter if you're off by 100 trillion years.