My initial question had lots of answers, as we can practically choose the middle square to be anything we want, and work outwards to the exterior edges, with the corners providing the flexibility needed.
So, as a bonus, I have added some more constraints. Same rules as before, with the outside sums only counting 2 sets of minuses.
8 7 3 --- --- --- --- 5 13 14 11 5 --- --- --- --- 7 11 10 13 7 --- --- --- --- 8 11 9 14 8 --- --- --- --- 5 6 9
Can you now solve the grid?