Parametric intersection curve of surfaces in PGA or CGA

My problem is to find the intersection of a torus with a sphere in PGA. I could parametrize them following Steven’s blog-post: Torus = Circle * Circle / Steven De Keninck | Observable.
Both the torus and sphere have two parameters (either simply in terms of motors or points after applying the motor to the origin) and their intersection using the outer product in PGA gives a 4 parameter element while it should be of only one parameter. I can try to loop over the parameters to find points of intersection but I might miss some points if I have to intersect it with a third element. So, I was wondering if there is a better way (in CGA or PGA) to get the parametric representation of the intersection curve.