You can open the file for both read and write, but that can be tricky. Better to create a new file and rename to old file name.

use strict;
use warnings;
use File::Copy;

my $infilename = 'Pull-2015-08-15-23.txt';
my $outfilename = 'new.file';
my $find = '20150518';
my $replace = '18 May 2015';

open $infile,'<',$infilename;
open $outfile,'>',$outfilename;
while (my $line = <$infile>) {
  $line =~ s/$find/$replace/;
  print $outfile $line;
}
close $infile;
close $outfile;
move($outfilename,$infilename);
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You may find modules like Date::Parse and Date::Format useful to deal with dates in general, and not just this specific example.

Update:

use Date::Parse;
use Date::Format;

@time = strptime("20150518");
print strftime("%e %b %Y",@time);
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