Need formula instead of sorting

You're really limiting yourself by not using Pivot Tables and performing a sort on the data. Why these limitations (or preferences)?

I see your results table is in alphabetical order and this is not easily accomplished with a formula, especially given multiple entries exist.

You could used Advance Filter to extract a list of unique values (for the item names), copied to a new location and then perform the sum using SUMIF.

Or, considering sorting the original data in place, forcing blanks to the bottom and then using the built-in SUBTOTAL feature which will allow you to collapse the rows and show only the totals.

I don't understand why you aren't taking advantage of the applicable tools to get the results you need. Use a separate worksheet if necessary so that the original data is untouched.