.model small
.stack 
.data
.code
 
start:
mov ah,1  
int 21h
mov ah,2
mov dl,0ah
int 21h
push ax
mov ah,1
int 21h
mov ah,2
int 21h
pop bx
add ax,bx
aaa
add al,30h
mov dl,al
mov ah,2
int 21h
end start

.model small
.stack 
.data
.code
 
start:
	mov ah,1  
	int 21h		; DOS - Read character from StdIn (Key)
		; al=char read
 
;	mov ah,2
;	mov dl,0ah	; WRITE LineFeed ????
;	int 21h		; DOS - Write character to StdOut
;		; NOTE: AL is now destroyed! as LineFeed was written!
 
;;; BASED upon your error, and this next push....
	mov	ah,2
	mov	dl,al
	int	21h
 
	push ax		; Save Old Character
 
	mov ah,1
	int 21h		; DOS - Read character from StdIn (Key)
		; al = char read
 
	mov ah,2
	int 21h		; DOS - Write character to StdOut
 
	pop bx		; Restore Old Character
		; al = 2nd char   bl = 1st char
 
; You aren't doing BCD so why are you using the instruction AAA ?
 
;;;	add ax,bx
;;;	aaa
 
	mov	ah,0
	add al,bl
	daa			; Decimal adjust  High Nibble, Low Nibble
                       ;ah=high digit, al=low digit
 
	mov	dh,al	; Save lower digit
 
	mov	dl,ah	; Upper digit
	add	dl,30h
	mov ah,2
	int 21h		; DOS - Write Digit Upper ASCII
 
	mov dl,dh	; Lower Digit
	add	dl,30h
	mov ah,2
	int 21h		; DOS - Write digit Lower ASCII
 
 
 
	end start

;daa         ; Decimal adjust
aaa           ; Ascii adjust