Instructor with student reports NMAC with C182; which started takeoff from opposite end of the same runway. The pilot of the C182 had radio problems; which made the reporter unaware of his intentions. Each pilot turned to avoid the other when airborne.

Narrative

I was instructing a student in his new experimental aircraft. The student had just purchased the aircraft from the builder/former owner; and I was checking him out in the aircraft. We taxied to Runway 25; making appropriate announcements on the CTAF. We heard unintelligible transmissions on the radio frequency. After our run up; we taxied into position on Runway 25. The student had the controls and started the takeoff roll. As he lifted the tail; I saw an aircraft headed directly for us; using the opposite Runway 7. I said; 'I have the controls;' and the student released his controls. The other aircraft began banking right. By this time; we were airborne; and I banked the airplane to our right. The other aircraft passed by on our left side; about 500 FT away. After we passed; I called on the radio and asked if the other pilot was on frequency. An unintelligible transmission followed. I responded that the transmission was unreadable. Another unreadable transmission followed. The student and I continued our training flight without incident. In discussing the incident later with a lineman in the FBO; they said that aircraft (the 182) had been having radio problems. There is no line of sight between runway ends at ZZZ. Winds were mostly calm; but Runway 25 was slightly favored; according to the windsock.