To find the total number of waiters \( w \), you can use the relationship between the permanent staff and the temporary staff. The total number of waiters is given by the sum of the permanent staff and the temporary staff:
\[ w = 34 + t \]
Given that \( t = 10 \):
\[ w = 34 + 10 \] \[ w = 44 \]
Thus, the value of \( w \) when \( t = 10 \) is \( \boxed{44} \).