jq, 7150 bytes
map(add)|sort|.[0],range(length)as$i|.[$i+1]-.[$i]
Uses the Arnauld/xnor approach of sum then sort then pairwise differences. Raises an error, but only after the entire output has been streamed.
General solution, 71 bytes
sort_by(length)|while(any;.[0][0]as$i|map(del(.[index($i)]))[1:])[0][0]
WeWorks on lists with arbitrary content - we take the shortest prefix (which has a length of 1), remove it and remove its first (only) value from all remaining prefixes. This gives us a prefix list for the list's tail. We then repeat the process for that prefix list. This eventually gives us a prefix list for the target list and all its suffixes. We then take the first (only) value from the first (shortest) prefix in each of those lists, to get the elements of the target list in order.
jq, 71 bytes
sort_by(length)|while(any;.[0][0]as$i|map(del(.[index($i)]))[1:])[0][0]
We take the shortest prefix (which has a length of 1), remove it and remove its first (only) value from all remaining prefixes. This gives us a prefix list for the list's tail. We then repeat the process for that prefix list. This eventually gives us a prefix list for the target list and all its suffixes. We then take the first (only) value from the first (shortest) prefix in each of those lists, to get the elements of the target list in order.
jq, 50 bytes
map(add)|sort|.[0],range(length)as$i|.[$i+1]-.[$i]
Uses the Arnauld/xnor approach of sum then sort then pairwise differences. Raises an error, but only after the entire output has been streamed.
General solution, 71 bytes
sort_by(length)|while(any;.[0][0]as$i|map(del(.[index($i)]))[1:])[0][0]
Works on lists with arbitrary content - we take the shortest prefix (which has a length of 1), remove it and remove its first (only) value from all remaining prefixes. This gives us a prefix list for the list's tail. We then repeat the process for that prefix list. This eventually gives us a prefix list for the target list and all its suffixes. We then take the first (only) value from the first (shortest) prefix in each of those lists, to get the elements of the target list in order.
jq, 71 bytes
sort_by(length)|while(any;.[0][0]as$i|map(del(.[index($i)]))[1:])[0][0]
We take the shortest prefix (which has a length of 1), remove it and remove its first (only) value from all remaining prefixes. This gives us a prefix list for the list's tail. We then repeat the process for that prefix list. This eventually gives us a prefix list for the target list and all its suffixes. We then take the first (only) value from the first (shortest) prefix in each of those lists, to get the elements of the target list in order.