Balloon Flight Instructor reported striking an unseen power line that resulted in an unplanned landing.

Narrative

Evening flight on south side of airport. Launched [and] headed southwest at 8 MPH. This was an instruction flight so [I] had [the] student do 1 touch-and-go midway through flight. After that takeoff; [we] continued southwest and on approach to land with [the] sun in our eyes; we were proceeding to land on a property that was wide open. As we approached property; we had visual of power wire and could see a pole behind house but could not see wire between the house pole and the road. As the student continued to land; [there was] a wire [that] could not be seen as we came over the road. Our crew then alerted us of a power line in our path [so] at this time; I took controls from [the] student and deflated balloon at 35 ft.; which caused us to hit [the] wire with [a] limp envelope and slide down [the] wire on the front side. The weight of the envelope caused the wires to touch and pop fuse to house. Both me and my student exited balloon with proper care to not create an arc.Both me and student were fine with no injuries. Aircraft has no damage but will be inspected before next flight. Power company came out and dropped line so we could retrieve envelope without damage to it or wire to house. Factors that led to this: Sun in our eyes was main issue. White cotton field really hid wire from point of view. X.XX miles total flight distance.