The diagonal of a face is √2 times the length of a side. If your diagonal is the diagonal of a face, the length of an edge of the cube is

10/√2 = 5√2.

The space diagonal of a cube is √3 times the length of a side. If your diagonal is the diagonal between opposite vertices through the center of the cube, the length of an edge is

10/√3 = (10√3)/3

10/√2 = 5√2.

The space diagonal of a cube is √3 times the length of a side. If your diagonal is the diagonal between opposite vertices through the center of the cube, the length of an edge is

10/√3 = (10√3)/3