What have you tried? In what way does it not work?

Does this do what you mean:

open(TMPFILE,"<page.html") || die "Cant open: $!";
while (<TMPFILE>) 
{
    chomp; 
    my $myFile = join('',<TMPFILE>);

    if ($myFile =~ /'(\d{3})wordONE/){
        $data = $1;
    }

    if ($myFile =~ /(\d{3})wordTWO/) {
        $data2 = $1;
    }
  }
close TMPFILE;
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You can combine the two if statements into an if .. elsif to speed things up slightly if you assume that no line will match both your patterns.

Update: While this does combine your two while loops I don't really expect this to do anything sensible (are you sure it works in the version that you had?)