9567 + 1085 = 10652
Reasoning (this is what went on my mind chronologically, so I'll just copy/paste

__S-E-N-D
__M-O-R-E
M-O-N-E-Y
s + 1 = 10 + o = 10 or
s + 1 = 10 + o = 11, which means: o = 1 (rejected)
=>
s + 1 = 10 =>
o = 0 => e + o < 10 =>
s = 10 - 1 = 9
(if e + o = 10, n = 0 so no way in hell)
======================================================
e + o = n and o = 0 => e + o + 1 = n
=> n = e + 1
=>
n + r = 10 + e, or
n + r = 10 + e - 1
If:
e + 1 = e + 10 - r => r = 9 (rejected)
e + 1 = e + 10 - 1 - r =>
r = 8
n + 8 > 10 => n > 2
=> n -> [4, 5, 6, 7], e -> [3, 4, 5, 6]
Because n = e + 1
n + 8 = e + 1 + 8 = (10 + e) - 1 => d + e > 10
However, y can't be: 0, 1, 5, 6, 7, 8, 9 => y -> [2, 3, 4]
If y = 2 => d + e = 10 + 2 => d = 7, e = 5, n = 6
check: 9567 + 1085 = 10652 (correct)
If y = 3 => d + e = 10 + 3 => d = 7, e = 6, n = 7 (rejected)
If y = 4 => d + e = 10 + 4 => even larger so nothx.