Formula to search cells/columns containing specific text

Hi,

I would like to search on 2 columns, to see if each cell in Column B contains text from any cell in Column A.

For example, IF the text in Column B (Email Address), Row 2 contains text from any cell in Column A (Domain) = True. Below is an example:

(A) DOMAIN NAME | (B)EMAIL ADDRESS | (C)TRUE OR FALSE?
hotmail.com | kara@web.com | TRUE
msn.com | mike@site.com | TRUE
web.com | jess@myaddy.com | FALSE
domain.com | sara@aol.com | TRUE
aol.com | ted@domain.com | TRUE
site.com | mark@domain.com | TRUE

I am currently using this formula:
=IF(ISNUMBER(SEARCH($A:$A,E2)),"TRUE","FALSE")

but it doesn't appear to be working. It only works if the matching rows are adjacent to each other. As you can see from the example above, the matching domains could be in any row, any cell.

Would anyone know the correct formula for this? I've searched everywhere Thank you!