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Let the two whole numbers be x and y.

then for you to not be confuse let's use this...

a. the product of two whole number is 364

b. difference of the numbers is 15
x - y=15

c. their sum which is the one we needed to find out

Okay so first let's find out what are the two whole numbers.

Let's use letter b, representing x-y=15
x=y+15 (we use the transposition method ot addition property of something)

then substitute the value of x on letter a,
(y+15)y=364 (then we distribute y to the value of x)
y^2 + 15y=364 ( note. the ^ thing is like raise to the power of something then again we transpose.)
y^2 + 15y - 364=0 (we use zero property of I don't know.)

After that we use factoring.
Think about possible factors of 364 and try doing trial and error but I'll help you with this so let's continue, so as I was saying, after figuring what factors will match the solution, which is 28 and 13. we make sure it will match up the equation above.

You can use foil method in solving this. (y+28) (y-13) =y^2 + 15y -364

and tadaah! 28 and 13 are the factors.

so let's do the zero property of something and do the subraction and addition property of equality)

(y+28) (y-13)
y+28=0 y-13=0
y+28-28=-28 y-13+13=+13
y=-28 y=13

but because it is always the positive one we get then the second whole number we need is 13.

After that we substitute the value of y which is 13 to letter b to find the first whole number .

x=15+13 (we transpose)

then let's see the results...
since x=28 and y=13
a. xy=364

b. x-y=15

c. x+y=?

so the sum of both whole numbers is 41.

I hope this help even though I suck at explaining. P.S. Hope too that you understand my weird explanation. ^__^