#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;


while (<DATA>)
{
   my %hash = /\s*(.*?)="(.*?)"/g;
   print Dumper \%hash;
}

=Prints:
$VAR1 = {
          'value' => '2017-06-03T11:27:23+01:00',
          'type' => 't',
          'desc' => 'Time file was created.',
          'ord' => '3',
          'Attr num' => '101',
          'name' => 'Created'
        };
=cut


__DATA__
Attr num="101" name="Created" desc="Time file was created." type="t" o
+rd="3" value="2017-06-03T11:27:23+01:00"
[download]

What is the simplest way of analysing the line to get the hash data?

Here's an SSCCE showing this by combining split with hash assignment. Note that this is to answer precisely the question you asked - namely it is the simplest method. That doesn't mean that it is the most efficient or secure or robust or best documented or the winner in any other criterion.

#!/usr/bin/env perl 
use strict;
use warnings;
use Test::More tests => 1;

my $in = q/Attr num="101" name="Created" desc="Time file was created."
+ type="t" ord="3" value="2017-06-03T11:27:23+01:00"/;
my %want = (
        'Attr num' => 101,
        name       => 'Created',
        desc       => 'Time file was created.',
        type       => 't',
        ord        => 3,
        value      => '2017-06-03T11:27:23+01:00'
);

my %have = split (/="|" ?/, $in);
is_deeply (\%have, \%want);
[download]

Update: typo fix (thanks, choroba)

my %datahash; 
while (my $line=<DATA>) { 
  chomp $line; 
  $line=~s/^\s+//; 
  $line=~s/\s+$//; 
  my ($var,$val0)=split('=',$line,2); 
  $val0='' unless (defined $val0); 
  if ($val0=~m/^\"(.*)\"$/) {  $datahash{$var}=$1;} 
  else {$datahash{$var}=$val0;} 
} 
use Data::Dumper; 
print Dumper({datahash=>\%datahash});
__DATA__
Attr num="101" 
name="Created" 
desc="Time file was created." 
type="t" 
ord="3" 
value="2017-06-03T11:27:23+01:00" 
noeq
noval=
noquotes=noquotes
[download]

Result

$VAR1 = {
          'datahash' => {
                          'name' => 'Created',
                          'Attr num' => '101',
                          'noeq' => '',
                          'noquotes' => 'noquotes',
                          'ord' => '3',
                          'noval' => '',
                          'value' => '2017-06-03T11:27:23+01:00',
                          'desc' => 'Time file was created.',
                          'type' => 't'
                        }
        };
[download]

A small point:

  chomp $line;  #### not needed with below ###
  $line=~s/^\s+//; 
  $line=~s/\s+$//; # this deletes all line ending char's
                   # so the chomp is unnecessary.
[download]

Something else that immediately occurs to me:   “is this XML?”

For instance, if the data actually looked like:

<Attr num="101" name="Created" desc="Time file was created." type="t" ord="3" value="2017-06-03T11:27:23+01:00"></Attr>

And even if it isn't XML, you could jam it into XML in order to take advantage of existing XML parsing facilities. To wit:

use XML::Simple;

while (<>)
{
    chomp;
    my $hashref = XMLin("<$_/>");
    ...
}
[download]