Answer

The two words that solve this puzzle are BLUEBELL and PEARTREE. 

Place the letters as follows: B 3-1, L 6-8, U 5-3, E 4-6, B 7-5, E 2-4, L 9-7, L 9-2. 
This means that you take B, jump from 3 to 1, and write it down on 1; and so on. 
The second word can be inserted in the same order. 
The solution depends on finding those words in which the second and eighth letters are the same, and also the fourth and sixth the same, because these letters interchange without destroying the words. MARITIMA (or sea-pink) would also solve the puzzle if it were an English word.