Can you install SQL Server Express (x86) on Windows 10 (x64 bit)?

The short answer is YES.

A x32 bit SQL Server Express Advanced and a x64 bit SQL Server 2016 SP1 are both installed on a Dell Inspiron laptop.

Here are the responses to the command:

SELECT @@version in a query launched by both of these versions:

(No column name)
Microsoft SQL Server 2012 - 11.0.2100.60 (Intel X86)   Feb 10 2012 19:13:17   Copyright (c) Microsoft Corporation  Express Edition on Windows NT 6.2 (Build 9200: ) (WOW64)

(No column name)
Microsoft SQL Server 2016 (SP1-GDR) (KB3210089) - 13.0.4202.2 (X64)   Dec 13 2016 05:22:44   Copyright (c) Microsoft Corporation  Developer Edition (64-bit) on Windows 10 Pro 6.3 (Build 15063: )

They can co-exist as shown: