Judging by your data, it looks like you only need to keep track of one line (not 4): the line above the +.

use warnings;
use strict;

my $prev;
while (<DATA>) {
    chomp;
    if (/\+/) {
        print length($prev), "\n";
    }
    $prev = $_;
}

__DATA__
@HWI-ST591:68:D0DBPABXX:5:1101:1197:2084 1:N:0:
GGTAGTTCGACCGTGGAT
+
B@@FFEFFHDHHFHIJJE
@HWI-ST591:68:D0DBPABXX:5:1101:1086:2085 1:N:0:
GCTGGAACTTGGCAAAGAAGAGAG
+
@@@FFEFFGHHHH@@FEHBEHJGG
[download]

prints...

18
24
[download]

See also:

• perldoc perlintro
• perldoc -f chomp
• length