You can use the Import wizard to load your data. The Import/Export wizard actually uses SSIS to do the work. But if your goal is to avoid learning SSIS, then just do not save the package.
Simple way to import data into SQL Server
That MSSQLtips article walks you through setting up the import and then run the data into your SQL Server destination.
If you want to reuse the package (which is probably a good idea) there is a save option that allows you to save the SSIS package that was internally generated and use it again and again.
However, if the Linked Server approach is the way you want to go, there is a tutorial here:
Excel Import to SQL Server using Linked Servers
This is somewhat more complex to set up, but should work OK.
UPDATE: based on your comment about coordinating two transactions you might find it simpler to import the data into two staging tables. (You would most likely truncate those tables before each load.) The table
Stage01 receives one load and the table
Stage02 receives the other load.
Then, now that both data sets are in their own tables, you can join between
Stage02 data sets to insert the resolved data into your operational database tables. This would likely simplify the processing of the two data sets.