Some solutions:
3875+1405=5280, T=3, A=8, K=7, E=5, H=1, O=4, M=0, X=2;
1875+3405=5280, T=1, A=8, K=7, E=5, H=3, O=4, M=0, X=2;
1325+4605=5930, T=1, A=3, K=2, E=5, H=4, O=6, M=0, X=9;
4325+1605=5930, T=4, A=3, K=2, E=5, H=1, O=6, M=0, X=9;
1985+3705=5690, T=1, A=9, K=8, E=5, H=3, O=7, M=0, X=6;
3985+1705=5690, T=3, A=9, K=8, E=5, H=1, O=7, M=0, X=6.
1076+5326=6402, T=1, A=0, K=7, E=6, H=5, O=3, M=2, X=4;
5076+1326=6402, T=5, A=0, K=7, E=6, H=1, O=3, M=2, X=4.
1306+5426=6732, T=1, A=3, K=0, E=6, H=5, O=4, M=2, X=7;
5306+1426=6732, T=5, A=3, K=0, E=6, H=1, O=4, M=2, X=7.
1057+6247=7304, T=1, A=0, K=5, E=7, H=6, O=2, M=4, X=3;
6057+1247=7304, T=6, A=0, K=5, E=7, H=1, O=2, M=4, X=3.
1057+6847=7904, T=1, A=0, K=5, E=7, H=6, O=8, M=4, X=9;
6057+1847=7904, T=6, A=0, K=5, E=7, H=1, O=8, M=4, X=9.
6387+1547=7934, T=6, A=3, K=8, E=7, H=1, O=5, M=4, X=9;
1387+6547=7934, T=1, A=3, K=8, E=7, H=6, O=5, M=4, X=9.
5617+2347=7964, T=5, A=6, K=1, E=7, H=2, O=3, M=4, X=9;
2617+5347=7964, T=2, A=6, K=1, E=7, H=5, O=3, M=4, X=9.
5837+1247=7084, T=5, A=8, K=3, E=7, H=1, O=2, M=4, X=0;
1837+5247=7084, T=1, A=8, K=3, E=7, H=5, O=2, M=4, X=0.
There are more solutions.
There appear to be no solutions if we restrict the range of digits to 1-8.
The starting point is M, which must be an even number: 0, 2, 4, 6, 8. From this E could be 3, 4, 5, 6, 7, 8, 9.