Find the Vertices of an Ellipse Given Its Foci and Distance Between Vertices

I need to find the coordinates of two vertices with focal points of (2,6) and (8,-2) and the distance between the vertices is 18.

I was able to calculate the center of the ellipse which is the midpoint of the foci: (5,2). I also know that that the a value (the distance from one of the vertices on the major axis to the center) is going to be 9 since the c value is 5. I can therefore say that whatever the coordinates of the vertices are must be 4 units away from the two focal points. However, I am not able to get any further than that in finding the coordinates of the vertices. Any help will be greatly appreciated.

I need to find the coordinates of two vertices with focal points of (2,6) and (8,-2) and the distance between the vertices is 18.

I was able to calculate the center of the ellipse which is the midpoint of the foci: (5,2). I also know that that the a value (the distance from one of the vertices on the major axis to the center) is going to be 9 since the c value is 5. I can therefore say that whatever the coordinates of the vertices are must be 4 units away from the two focal points. However, I am not able to get any further than that in finding the coordinates of the vertices. Any help will be greatly appreciated.