You should be able to do this by creating a language override, as the content of the Joomla system emails comes from language files. I'm not sure exactly what notification you want to override, but take a look at the file
Remember you should never edit core Joomla files. Locate the string(s) you need, and create an override.
You can create an override from the Joomla admin area. Under "Extensions" click on "Language Manager".
Or do it manually but creating the following file (if it doesn't already exist):
In this file you can add your overrides, and they will not be deleted when you update Joomla.
An easier alternative would maybe be to use a Joomla form component (I like BreezingForms a lot, but there are many other alternatives). It's possible to configure both user and admin emails, and even attach additional files to the message, like a PDF or image.