Air carrier pilot reported a NMAC with an aircraft at 28;000 ft. while in IMC.

Narrative

We leveled off at 28;000 feet. I was listening to the MYR ATIS at the time; but was aware of ATC making altitude inquiries to an opposite direction Aircraft X. ATC was attempting to verify that Aircraft X was level at 27000 and that his altimeter was set to 29.92. The aircraft verified that he was at 27;000 and his altimeter was 29.92. However; he kept climbing. This began at a distance of 10 miles. Aircraft X continued to climb and we received an RA caution message. At this time; I paid sole attention to the TCAS alert and ATC. Suddenly; we received a TCAS warning with instructions to climb. The TCAS climb rate required as 2;200 feet per minute at 28;000 feet. We immediately complied with TCAS and I saw that we went over the top of Aircraft X just 300 feet below. Had we not immediately complied with the TCAS; it is likely that a mid air collision would have occurred. After the event was over; we asked ATC for information about the aircraft we just went over. They gave us a Center number to call; and we called it when safely on the ground. From the call; we learned the aircraft type; tail number; and that we had a closure rate of over 900 knots. We never saw Aircraft X as we were in IMC through the entire event.