Subtracting to 2008

Can you work out the sum of the missing digits in this subtraction?
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Problem



In this subtraction, $P$, $Q$, $R$ and $S$ are digits. What is the value of $P + Q + R + S\;$?

                          
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Subtracting to 2008
 

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.