Sorry, for some reason I didn’t get an e-mail notification regarding your post from last week.
You want to look for a file called header.php. You may be able to find it by going to Appearance → Editor. Normally you don’t want to edit the theme files this way, but it looks like your theme is custom-made, so it should be OK. However, I would keep a back-up of any files that you modify by copying the contents and pasting into a text file.
Hopefully you have some knowledge of HTML. Inside header.pho, you want to look for the link to the image file, something that looks like this:
<div id="header-img" class="alignright">
<img src="https://www.theelenchusinstitute.com/wp-content/themes/elenchus-institue/img/contact-us-img.jpg" alt="Elenchus Institue">
</div>
You can either change the URL pointed to by the src attribute, or you can upload a new image to the same location, with the same file name, and over-write the existing image.
As far as adding additional text goes, do you want to squeeze in another <div>
element between the logo and quote on the left, and the image on the right?