How do you find marginal revenue if you don't have a production function?
Here are some hints. Either solve the profit function in terms of $p$, substituting out all references to $q$ (recall that $D(p) = q$), or solve the profit function in terms of $q$, substituting out all references to $p$. Then you'll find that the profit function is concave and the differentiated with respect to $p$ in the first case or $q$ in the second case will give you the profit maximizing solution.

EDIT: Yeah, $a = 2q + 10$ looks correct. Just solve the equation for $q$ and the interpretation is clear. That is, the quantity produced is $q = (a - 10)/2$. If you want to know the price, then just substitute $q$ in for $D(p)$ like so: $a - p = D(p) = q = (a - 10)/2$.