One clear-span method that can be used is to though-bolt a ledger board to the brick walls on all sides at the 10 foot height.
You could then use joist-hangers to fasten the floor joists to the ledger.
The down-side to this approach is that the bolts will be exposed on the exterior of the brick walls.
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Another clear-span method would be to frame four walls around the interior on the 1st floor on top of which you can install your floors joist for the upper story.
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