Assume the two terms are consecutive terms in an ascending arithmetic progression.
The general term in the progression is a+nd where a=first term, n denotes the number of the term and d is the constant difference. The difference in consecutive terms is d=389003-388957=46.
So a+46n=388957 and a+46n+46=389003.
We can write the first equation a+46n=8455*46+27, a-27=46(8455-n).
If a-27=0, 46(8455-n)=0 so n=8455 and a=27. Therefore the series could be 27, 73, 119, 165, ..., 388957, 389003, .... This is not the only solution.
Another possibility is 4, 27, 50, 73, 96, 119, 142, 165, ..., 388957, 388980, 389003, ..., where the common difference is 23.