The sum of two numbers is 19, while the difference between the two numbers is 3. Find the smaller number out of these two numbers.

Let the two numbers be x and y, where x>y.
According to the problem:

x+y=19

x−y=3

Subtracting equation (2) from equation (1):

(x+y)−(x−y)=19−3
2y=16
y=8
Thus, the smaller number is 8.