Well, once you've derived unary exp and ln you can get subtraction, which then gets you unary negation and you have addition.

It's basically using the "-" embedded in the definition of the eml operator.

Table 4 shows the "size" of the operators when fully expanded to "eml" applications, which is quite large for +, -, ×, and /.

Here's one approach which agrees with the minimum sizes they present:

        eml(x, y             ) = exp(x) − ln(y) # 1 + x + y
        eml(x, 1             ) = exp(x)         # 2 + x
        eml(1, y             ) = e - ln(y)      # 2 + y
        eml(1, exp(e - ln(y))) = ln(y)          # 6 + y; construction from eq (5)
                         ln(1) = 0              # 7

              eml(ln x, exp y) = x - y          # 9 + x + y

                   x - (0 - y) = x + y          # 25 + {x} + {y}

Don't know adding, but multiplication has diagram on the last page of the PDF.

xy = eml(eml(1, eml(eml(eml(eml(1, eml(eml(1, eml(1, x)), 1)), eml(1, eml(eml(1, eml(y, 1)), 1))), 1), 1)), 1)

From Table 4, I think addition is slightly more complicated?