c:\@Work\Perl\monks>perl -wMstrict -le
"use 5.010;
 ;;
 use Regexp::Common qw(number);
 ;;
 my @lines = (
   qq{Line 1 = 0154.45 +02 13.56 +03 64.35 \n},
   qq{Line 2 = +09 23.12 +10 8798 \n},
   );
 ;;
 my $prefix = qr{ \G (?: \A Line \s* \d+ \s* =)? \s+ }xms;
 for my $line (@lines) {
   my @numbers = $line =~ m{ $prefix \K  $RE{num}{real} }xmsg;
   printf qq{'$_'  } for @numbers;
   print '';
   }
"
'0154.45'  '+02'  '13.56'  '+03'  '64.35'
'+09'  '23.12'  '+10'  '8798'