Question 987739
n=p(n) +s(n).
<pre>

Let the tens digit be t and the units digit be u:

p(n) = tu;  s(n) = t+u; n = 10t+u 

10t+u = tu + t+u

9t-tu = 0

t(9-u) = 0

t=0;  9-u=0
        9=u

The tens digit can't be 0.

So the units digit is 9.

Substituting:

{{{9t-tu=0}}}
{{{9t-t(9)=0}}}
{{{9t-9t=0}}}
{{{0t=0}}}

Any digit but 0 can be the tens digit.

So there are nine solutions.

19 = 1×9 + 1+9 =  9+10 = 19
29 = 2×9 + 2+9 = 18+11 = 29 
39 = 3×9 + 3+9 = 27+12 = 39
49 = 4×9 + 4+9 = 36+13 = 49
59 = 5×9 + 5+9 = 45+14 = 59
69 = 6×9 + 6+9 = 54+15 = 69
79 = 7×9 + 7+9 = 63+16 = 79
89 = 8×9 + 8+9 = 72+17 = 89
99 = 9×9 + 9+9 = 81+18 = 99

Edwin</pre>