Missing numbers in arithmetic sum Challenge

Giving a valid arithmetic sum with some missing numbers, output the full expression.

Example: 

    1#3                 123
+   45#     =&gt;     +    456
--------            --------
    579                 579


Input


Expression format can be an array ["1#3", "45#", "579"], a string "1#3+45#=579", or 3 inputs f("1#3","45#","579")


Output 


Same as input
You don't need to output the result 


Notes


The missing numbers are going to be represented using # or any other constant non-numeric character you want
Assume result wont have a missing number
Assume Input/Output consist in 2 terms and a final result
Assume both term > 0 and result >= 2
There might be multiple solutions. You can output anyone as long as the sum result match


Test Cases with possibly outputs (pretty format)

    #79                     879
+   44#         =&gt;      +   444
--------                --------
    1323                   1323

    5#5                     555
+   3#3         =&gt;      +   343
--------                --------
    898                     898

      #                       1
+     #         =&gt;      +     1
--------                --------
      2                       2

    ###                     998
+   ###         =&gt;      +     1     PD: there are a lot of possible outputs for this one
--------                --------
    999                     999


    123                     123
+     #         =&gt;      +     1
--------                --------
    124                     124


      9                       9
+    #6         =&gt;      +    46
--------                --------
     55                      55


    #123651                     1123651
+      #98#         =&gt;      +      7981
------------                -----------
    1131632                     1131632




Standard code-golf rules apply
Brachylog, 22 16 bytes

{Ṣ∧Ị∋|}ᵐ²ịᵐ.k+~t


Try it online!

-6 bytes thanks to @Fatelize

Explanation

{Ṣ∧Ị∋|}ᵐ²ịᵐ.k+~t
{     }ᵐ²                   #   for each letter in each string
 Ṣ∧Ị∋                       #       if " " return a digit; else input
     |                      #
         ịᵐ                 #   cast each string to number
            k+              #   the sum of all but the last one
              ~t            #       is equal to the last one
           .                #   output that list