Try saving this xml file and opening it again:

<?xml version="1.0" encoding="UTF-16LE"?>

________________________________
From: J S <jszabo_98@hotmail.com>
Sent: Thursday, May 16, 2019 7:15 PM
To: Eli Zaretskii
Subject: Re: bug#35766: emacs saves utf-16 le xml files as utf-16 be

Try saving this xml file and opening it again:

<?xml version="1.0" encoding="UTF-16LE"?>


________________________________
From: Eli Zaretskii <eliz@gnu.org>
Sent: Thursday, May 16, 2019 6:22 PM
To: J S
Cc: 35766@debbugs.gnu.org
Subject: Re: bug#35766: emacs saves utf-16 le xml files as utf-16 be

> From: J S <jszabo_98@hotmail.com>
> Date: Thu, 16 May 2019 17:11:21 +0000
>
> Xml files with this tag are saved as utf-16 be by emacs, even if the file was originally utf-16 le.  Using
> "UTF-16LE" instead will break the encoding and remove the BOM.
>
> <?xml version="1.0" encoding="UTF-16"?>

Did you try using utf-16le-with-signature?

Or maybe I don't understand the scenario: would you please describe a
full reproduction recipe, starting from "emacs -Q"?

Thanks.