The Google search bar (widget) on the home screen, lets you search for content both in your device's memory or internet. To remove / add Google search widget to home screen on HTC 10, do as follows
1. Press the Home Button to make sure you are on the home screen
2. Press and hold your finger on an empty place to open the Personalize menu
3. Select the Add Apps and Widgets option
4. Make sure you are viewing the Widgets category (you can change it from the top bar using the drop down menu. Other options are Apps and Shortcuts)
5. Now, you should see the list of all your installed home screen widget. Simple scroll down to find the Google Search Bar widget
6. Once you find it, drag and drop to the home screen and you are all DONE.