WordPress - Show updated date as well if post was modified

entry_meta.php

if ( ! function_exists( 'aa_entrymeta' ) ) :
/**
 * Prints HTML with meta information for the current post-date/time and author. If post was updated, it also prints
 * the date of the update.
 */
function aa_entrymeta() {
	$time_string = '<time class="entry-date published updated" datetime="%1$s">%2$s</time>';
  $update_time_string = '<time class="updated" datetime="%s">%s</time>';
    
    $time_string = sprintf( $time_string,
        esc_attr( get_the_date( 'c' ) ),
        esc_html( get_the_date() )
	  );
    
	$posted_on = sprintf(
		_x( 'Posted on %s', 'post date', 'codeaurooba' ),
		'<a href="' . esc_url( get_permalink() ) . '" rel="bookmark">' . $time_string . '</a>'
	);

	$byline = sprintf(
	  _x( 'by %s', 'post author', 'codeaurooba' ),
		'<span class="author vcard"><a class="url fn n" href="' . esc_url( get_author_posts_url( get_the_author_meta( 'ID' ) ) ) . '">' . esc_html( get_the_author() ) . '</a></span>'
	);
    
	if ( get_the_time( 'U' ) !== get_the_modified_time( 'U' ) ) {
		$update_time_string = sprintf( $update_time_string, 
      esc_attr( get_the_modified_date( 'c' ) ),
      esc_html( get_the_modified_date() )
    );
        
    $updated_on = sprintf(
      _x( 'Updated on %s', 'updated date', 'codeaurooba' ),
  		'<a href="' . esc_url( get_permalink() ) . '" rel="bookmark">' . $update_time_string . '</a>'
  	);
        
    echo '<span class="posted-on">' . $posted_on . '</span><span class="updated-on">' . $updated_on .'</span><span class="byline">' . $byline . '</span>';    
	} else {
    echo '<span class="posted-on">' . $posted_on . '</span><span class="byline">' . $byline . '</span>';   
    }

}
endif;