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Assuming the files are in the current directory, ad that you're using bash:

files=( T*.CDT )
grep 'FCE-Error' "${files[-1]}"

This would grep the most recent .CDT file for the string. You could do the same for the other type of file.

The shell globbing pattern T*.CDT expands to all matching filenames sorted lexicographically, and since you are using sane filenames (with proper timestamps that sorts properly), the last of these will be the latest file.

To mail an alert if the string is found:

files=( T*.CDT )
if grep -q 'FCE-Error' "${files[-1]}"; then
    mail -s 'Alert' someperson@example.com <<END_MESSAGE
We've found "FCE-Error" in ${files[-1]}, do something!
END_MESSAGE
fi