Light aircraft instructor pilot reported rejecting the takeoff on Runway 28 at FME airport when he noticed another aircraft on final approach to Runway 10.

Narrative

Was departing VFR from FME. Made appropriate radio call on CTAF and visually made sure the pattern was free of other aircraft. Took active runway 28 and made radio call on CTAF stating my intentions of departing VFR off of 28. We take the runway and add full power and start rolling. As we are rolling we notice what appears to be an aircraft appear very low over the trees off of runway 10. I took controls from my student and pulled power and started braking heavily; while also calling on CTAF for the traffic to go-around. The traffic continued on their final approach on 10 and did not execute a go-around till about what I estimate being 50 feet. We stopped on the runway and taxied off. I called repeatedly over CTAF for the aircraft and they did not respond to us until about 30 seconds after. I asked had they heard or seen us and they said they had heard us and that 'we can hear you now.' I asked if they were IFR and when they had gotten switched to CTAF from approach. They stated they had switched over to the CTAF prior to the FAF. Winds were clearly favoring 28. We taxied back to 28 and departed and the aircraft landed after us in runway 10. We departed to the south and did not hear from them again.The other pilot is not based at the field and it did not seem like they were on the appropriate frequency and he sounded very nervous on the radio.