Remember that the decimal number system is a positional number system. For decimal, that means ones place, tens place, etc.
Let the number be xy [note: x is a digit in tens place and y is another digit in ones place]
Learn to translate the words into formulas:
"When you reverse the digits in a certain two-digit number you increase its value by 45." means
10y + x = (10x + y) + 45 [eq1]
"the sum of its digits is 11" means x + y = 11 [eq2}
Now, solve (let's use substitution):
y = 11-x [from eq2]
Put that into eq1:
10y + x = (10x + y) + 45 [eq1]
10(11-x) + x = 10x + (11-x) + 45
110 - 10x + x = 10x + 11 - x + 45
110 - 9x = 9x + 56
-18x = -54
x = 3
Now, put that into either equation to find the value of y:
3 + y = 11 [eq2]
3 + y = 11
y = 8
The number is 38.
Check:
Is 83 = 38 + 45 ?
83 = 83 ?yes
Is 3 + 8 = 11 ?
11 = 11 ?yes