Why lea give different results with add?

Question

can you please help me, I have this ams code:

; subs two long number
;    rsi -- address of minuend (long number)
;    rdi -- address of subtrahend (long number)
;    rcx -- length of long numbers in qwords
; result:
;    sub is written to rdi
sub_long_long:
                push            rdi
                push            rsi
                push            rcx

                clc
.loop:
                mov             rax, [rsi]
                lea             rsi, [rsi + 8]
                sbb             rax, [rdi]
                mov             [rdi], rax
                lea             rdi, [rdi + 8]
                dec             rcx
                jnz             .loop

                pop             rcx
                pop             rsi
                pop             rdi
                ret

now, if I'm change lea rsi, [rsi + 8] to add rsi, 8 program give me wrong result on pretty big numbers, e.g.:

10000000000000000000000000000000000000000000000000000000000000000000 1000000000000000000000000000 9999999999999999999999999999999999999999000000018446744073709551616

Why is it happening?