The average of the ages is 10, so
$$ \frac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6 }{6} = 10$$
Simplifying the expression we have:
$$ x_1 + x_2 + x_3 + x_4 + x_5 + x_6= 60 \tag 1$$
Given the difference between the youngest and oldest ages:
$$x_{max}-x_{min} = 8$$
This information cannot be used to solve for the specific ages of the birds. More information is needed to find the exact ages.