Sorry, my bad. Try this.

#! perl -slw
use strict;

my $re =  qr[
    <!--QBlastInfoBegin    # Match the start of comment
    \s+                    # 1 or more whitespace including newlines
    RID                    # 'RID' literal
    \s+                    # One or more whitespace
    =                      # '=' 
    \s+                    # more whitespace
    (                      # start capturing to $1
         [\d-]+            # 1 or more '0-9' or '-'
                         
    )                      # end capture
    \s+                    # yet more whitespace
    RTOE                   # 'RTOE' literal
    \s+                    # And more whitespace
    =                      # '=' literal
    \s+                    # more 
    (                      # start capture to $2
        \d+                # 1 or more digits
    )                      # end capture
    \s+                    # more whitespace
    QBlastInfoEnd          # the end token
    \s+                    # final whitespace (including newlines)
    -->                    # The end comment card
]x;                        # Ignore incidental spacing and comments in
+ regex.

my $html = do{ local $/; <DATA> }; Grab the data from <DATA> into a st
+ring


my( $RID, $RTOE ) = $html =~ $re; # Execute the regex and assign the c
+aptures to variables.

print "RID:$RID RTOE:$RTOE";  # Print the results.

__DATA__
<!--QBlastInfoBegin
  RID = 1055976860-01972-17207
  RTOE = 7
QBlastInfoEnd
-->
[download]

Without the verbose commenting, the (now tested and working) regex looks like this

my $re =  qr[
    <!--QBlastInfoBegin           \s+
     RID  \s+ = \s+ ( [\d-]+ )     \s+
    RTOE \s+ = \s+ ( \d+    )     \s+
    QBlastInfoEnd                 \s+
    -->
]x;
[download]

The +'s mean match 1 or more of the preceeding element. See perlre and perlretut for more.