How to install Firmware 1.10E on an EV3 home/retail edition brick
New answer (2020)
The V1.10E firmware is installed using the EV3 Device Manager web page. The instructions are not entirely clear, but if you visit the web page with Chrome (recommended), Safari, Edge, or Internet Explorer, click the Available Bricks (0) button and wait a very long time, it will eventually pop up a dialog asking to download and install an EV3 Device Manager program to your computer. The EV3 Connection Manager program runs in the background on your computer and communicates with the EV3 Connection Manager web page in the browser. After installing the separate background program, the web page will be able to connect to your EV3. Then you can use it to update the firmware. It does not appear that this method gives you the option of selecting which firmware file to use.
Old answer - for retired EV3 Lab software
You can get the 1.10E firmware from the LEGO Education website. Currently, this can be done by clicking the Download Firmware button at the bottom of this page.
In the EV3 programming software, make sure you have a project open (e.g. create a new empty project), then click Tools &gt; Update Firmware.
Click the Show Details button.

Then click Browse and select the firmware file that you downloaded.

Make sure your EV3 is connected via USB and powered on, then click Update Firmware.