How to add missing and value in Julia and get the value instead of missing

Given your requirements I would recommend you to define your own custom addition that would implement the rule you want:

julia> ⨨(::Missing, ::Missing) = missing
⨨ (generic function with 1 method)

julia> ⨨(x, ::Missing) = x
⨨ (generic function with 2 methods)

julia> ⨨(::Missing, x) = x
⨨ (generic function with 3 methods)

julia> ⨨(x, y) = x + y
⨨ (generic function with 4 methods)

julia> [1, 2, missing, missing] .⨨ [10, missing, 30, missing]
4-element Vector{Union{Missing, Int64}}:
 11
  2
 30
   missing

In my example ⨨ can be typed by \plustrif<tab> (you could use any other symbol that is accepted as operator instead).

This is the most efficient way to achieve what you want.

This is a somewhat unusual treatment of missing - if I understand you correctly you want missing to behave like a zero if added to another number, and like missing when added to another missing. Given that this is a bit unusual, I would just write it out explicitly:

julia> a = [1, missing, missing]; b = [2, 1, missing];

julia> ifelse.(ismissing.(a) .& ismissing.(b), missing, coalesce.(a, 0) .+ coalesce.(b, 0))
3-element Vector{Union{Missing, Int64}}:
 3
 1
  missing

coalesce replaces missing with 0 in the above, but the result of that addition is only used if either of the two values being added is nonmissing.