<?php printf( '<time datetime="%s">%s</time>', $order->get_date_created()->format( 'c' ), wc_format_datetime( $order->get_date_created() ) ); ?>

$date_modified = $order->get_date_modified();
echo sprintf( '<p>Order NO. %s (placed on <time>%s</time>)</p>',
    $order->get_order_number( ),
    $date_modified->date("F j, Y, g:i:s A T")
);

$date_paid = $order->get_date_paid();
if( ! empty( $date_paid) ){
    echo sprintf( '<p>Order NO. %s (placed on <time>%s</time>)</p>',
        $order->get_order_number( ),
        $date_paid->date("F j, Y, g:i:s A T")
    );
}

add_action( 'woocommerce_email_order_details', 'custom_processing_order_notification', 1, 4 );
function custom_processing_order_notification( $order, $sent_to_admin, $plain_text, $email ) {
    // Only for processing email notifications to customer
    if( ! 'customer_processing_order' == $email->id ) return;

    $date_modified = $order->get_date_modified();
    $date_paid = $order->get_date_paid();

    $date =  empty( $date_paid ) ? $date_modified : $date_paid;

    echo sprintf( '<p>Order NO. %s (placed on <time>%s</time>)</p>',
        $order->get_order_number( ),
        $date->date("F j, Y, g:i:s A T")
    );
}