Display post count on archive page in reverse order

You can give a try to this within a loop

<?php 
      echo $wp_query->found_posts - $wp_query->current_post ;
?>

$wp_query->found_posts gives the total number of posts found matching the current query parameters.

So the if there are 20 posts, result for each post should look like this

For 1st post it will display 20, i.e. 20-0=20
For 2nd post it will display 19, i.e. 20-1=19,
…
…
…
For 12th post it will display 9, i.e. 20-11=9, and
For 20th post it will display 1, i.e. 20-19=1,