Can I install IE7 and IE8 in Windows 10?

Virtual machines are available for just such scenarios (testing old versions of IE). You can find them at https://dev.windows.com/en-us/microsoft-edge/tools/vms/windows/

EDIT The URL for VMs in the approved answer has changed. It's now at:

https://developer.microsoft.com/en-us/microsoft-edge/tools/vms/

1. Open Internet Explorer.
2. Press F12 and select the Internet Explorer
   version to be emulated.