Teaser 2895: Spanish and Latin

From The Sunday Times, 18th March 2018 [link]

I have ten cards. For each card there is a number in Spanish on one side and a number in Latin on the other.

The Spanish numbers are CINCO, CUATRO, DIEZ, DOS, NUEVE, OCHO, SEIS, SIETE, TRES and UNO. The Latin numbers are DECEM, DUO, NOVEM, OCTO, QUATTUOR, QUINQUE, SEPTEM, SEX, TRES and UNUS. For each of the ten pairs of numbers, there are two letters in common. If I told you on how many cards the two numbers were consecutive, you should be able to work out all ten pairings. The Spanish numbers are written alphabetically.

What is the corresponding order for the Latin numbers?