Let x and y be the two numbers.
According to the question,
\(x + y = 10 5 \quad ....(\text{i})\)
\(x - y = 45 \quad ....(\text{ii})\)
Adding (i) and (ii), we get
\(2x = 150\)
\(x = \frac{150}2\)
\(\therefore x = 75\)
Now, substituting x = 75 in the equation (i)
\(x + y = 105\)
\(75 + y = 105\)
\(y = 105 - 75\)
\(\therefore y = 30\)
Therefore, the two numbers are 75 and 30.
