You almost have it. Two things are wrong:

1. You need to put $number into list context to retrieve $1
2. Read up the bit on character classes again in perlre, they allow you to match a range of single characters, you still need to quantify them if you want to match more than once. [ee] and [e] are equivalent and will both match a single character "e".

this will work:

($number) = $str =~ /abc\sdddd\s+(?:ee\s+)?(\d+)/;
[download]

As for your question about the two extended operators, they influence capturing of an expression in brackets. perlre really explains it the best way I know, though you may want to take a look at Mastering Regular Expressions which is a very worthwhile book to read when learning regular expressions.

Update:Removed "gs" as they're not necessary (thanks to prasadbabu for pointing that out)