my $txt = <<'EOF';
f834bkg94halUF9deju hHFDUO()NFRS432 DSFadsfg94hHFDUO()N
hfedls74d8oHFx constant=barney@gmail.com alUF9dejuH()NF
UO()NFRS432 DSFadsf4halUF9deju fedls74d8oH sfg94hHFDUOf
f834bkg94halUF9deju hHFDUO()NFRS432 DSFadsfg94hHFDUO()N
hfedls74d8oHFx constant=wilma@aol.com alUF9dejuH()NFui0
UO()NFRS432 DSFadsf4halUF9deju fedls74d8oH sfg94hHFDUOf
EOF

while ($txt =~ /constant=(\w+@\w+\.\w+)/g) {
  print "$1\n";
}
[download]

Prints what you want for me. To understand what it does note the /g flag used to match that allows to not reset the match at the beginning from call to call as a result of the while loop.