Hi Frederick, if the "other solid" is always an extrusion like you show here then creating the closed perimeter curve is probably the easiest method.

If you want to do that with the least amount of steps set up a keyboard shortcut for Ctrl+L to have this:
script: moi.geometryDatabase.selectLoop();

Then select 2 adjacent edge curves on the top face:


Push Ctrl+L to extend selection to all the edges on the outer boundary of the top face:


Now use Edit > Join to make the closed boundary curve.

If you don't want to make a boundary curve I guess you could take the solid and stretch it vertically so it is is longer than the other solid and do a boolean difference with it.

- Michael