Just count the spaces and add 1:
// No need to count markup.
$text = trim( strip_tags( get_the_content() ) );
$word_number = substr_count( $text"$text ", ' ' ) + 1;;
Another way, taking the old American double space tradition into account:
$word_number = preg_match_all( '~\s+~', $text"$text ", $m ) + 1;;