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:

In reply to Re: read nth lines in a text file by toolic
in thread read nth lines in a text file by adansonia

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