I don't change anything for the ringing 10, because I figure it was a good shot. If it happens frequently then I may tweak my entry angle, but the shot that leaves the ringing 10 will usually have a good carry percentage.
The flat 10 requires a change in entry angle. First, I usually try hitting the 1-3 slightly higher to send the 3 more to the right, which helps the 6 do it's job. On the flat 10 the 3 pin usually heads straight back, which sends the 6 sideways to lay in the channel.
Assuming your angle is good then I look at other causes for the flat 10, such as the ball losing energy too fast by finding friction too early. We are all different. We throw it with varying speeds, rev rates, rotation, etc., not to mention the myriad of different balls at our disposal. What works for one might not be the answer for you, but don't be afraid to try. Leaving 10 after 10 after 10 can drive you nuts if you let it.
I look at changing my angle this way: If all I am doing is shooting spares, I can tweak my entry angle and still make spares in the worst case scenario. If it works then all is fine again. Once you decide to change, then commit to it and be fearless so you'll release the ball well...