Since Carbide Create doesn’t allow composite paths to be handled as such in Boolean operations what you need to do is to edit the inner path to be larger an overlap the outer one where you want to remove geometry:
First add some nodes by punching out a corner along the straight line:
Then go into edit mode and arrange the nodes:
then select the outer shape and control click on the inner shape so that it’s the key object and do a Boolean Subtraction:
Attached.
joined lines.c2d (424.9 KB)