The sum of your teacher’s age and the age of the school principal is 95. the difference in your teacher’s age and the age of the school principal is 21. hell

So we know that the sum of their ages is 95, and the difference is 21. We don't know either of their ages, but we can do that with a little algebra. 

Defining some variables:

x = teacher's age
y = principal's age

From there, we can turn those sentences from the problem into mathematical statements. 

x + y = 95
x - y = 21

Next, we want to isolate the system of equations to get only one variable. We can do this by adding the two equations together.
In doing that, you'll get 2x = 116. 
Solving for x (divide both sides by two) will get you 58. 

Now you know your teacher's age (58). You can plug this back in to solve for your principal's age. 

58 + y = 95

Subtract both sides by 58 and you'll get 37 for the principal's age.

Teacher's Age: 58
Principal's Age: 37