A E R **O** + N E X **T** = R A R** E**

A E R **O** - N E X **T** = E X I **T**

=>** E=3T** (mod 10) **O=2T (**mod 10**)** (supposing same value for T in all words implicated: if no results should be found we will revoke these suppositions)

so T O E (possible values)

1 2 3

2 4 6

4 8 2

6 2 8

7 4 1

8 6 4

but

A E **R O** R A **R** **E**

** + = +**

A E **R O ** E X **I** **T**

=>either or E+T=10+2O or E+T+10=2O in the first case R=I+1 in the second case I=R+1. In both cases I, R neighboring digits

E+T+10=2O => **T O E = 4 8 2 **(with E+ T =10 + 2O is also possible T O E = 6 2 8 but E value is very high, see below)

Also:

**A** E R O + **N** E X T = **R** A R E

**A** E R O - **N** E X T = **E** X I T

=>**R>A>(N,E)**

**Collecting results: **

X=9

T O E=4 8 2

I=R+1 e R>A>(N,E)

**Ordering letters:**

**X=9; O=8; I=7; R=6; A=5; T=4; **and E,N=3,2,1

But as N has unique value => either: or (E=3 / 2 and N=1) or (N=3 and E=2 / 1)

**Solution**

**X=9; O=8; I=7; R=6; A=5; T=4; E=3, 2; N=1**