To use EXPLAIN, just add it to the front of your query and then run, i.e.
EXPLAIN SELECT DISTINCT T1.NO FROM TABLE1 T1
LEFT JOIN TABLE2 T2 ON T1.NO <> T2.NO
MySQL will not return the query results but will return information about how it's using the indexes to join the tables in the query.
The reason why your second query is taking so long is that it's matching the wrong thing. Consider these tables.
table 1
1
2
3
4
5
table 2
3
4
Your query will produce these results
t1.id t2.id
1 3
1 4
2 3
2 4
3 4
4 3
5 3
5 4
which is probably not what you want.
If you use this query:
SELECT DISTINCT T1.NO FROM TABLE1 T1
LEFT JOIN TABLE2 T2 USING (NO) WHERE T2.NO IS NULL
you will get these results
t1.id t2.id
1 NULL
2 NULL
5 NULL
i.e. all those rows in t1 which are not in t2.