#05AB1E, 4 bytes

δαOß

I know there is already an existing 4-bytes 05AB1E answer using the median builtin Åm, but I decided to post this alternative 4-byter without this builtin.

Try it online or verify all test cases.

Explanation:

δ     # Apply the following command double-vectorized on the given two arguments,
      # which will use the input-list twice implicitly, since the stack is empty:
 α    #  Absolute difference
      #  i.e. [1,10,100] → [[0,9,99],[9,0,90],[99,90,0]]
  O   # Sum each of these inner lists
      #  → [108,99,189]
   ß  # Pop and push the minimum of this list
      #  → 99
      # (after which this is output implicitly as result)

05AB1E, 4 bytes

δαOß

I know there is already an existing 4-bytes 05AB1E answer using the median builtin Åm, but I decided to post this alternative 4-byter without this builtin.

Try it online or verify all test cases.

Explanation:

δ     # Apply the following command double-vectorized on the given two arguments,
      # which will use the input-list twice implicitly, since the stack is empty:
 α    #  Absolute difference
      #  i.e. [1,10,100] → [[0,9,99],[9,0,90],[99,90,0]]
  O   # Sum each of these inner lists
      #  → [108,99,189]
   ß  # Pop and push the minimum of this list
      #  → 99
      # (after which this is output implicitly as result)