Given mean and variance of 7 observations are 8 and 16.

Five observations are 2, 4, 10, 12, 14.

Let the other two observations are x and y.

So 7 observations are : 2, 4, 10, 12, 14 ,x ,y

Now

       Mean =  (2+4+10+12+14+x+y)/7

=> 8 = (2+4+10+12+14+x+y)/7

=> 8*7 = 2+4+10+12+14+x+y

=> 56 = 42 + x+ y

=> x + y = 56-42

=> x + y = 14 ...................1

Again Given varience = 16

=> (1/7)*∑ (xi - mean)² = 16          (7<=i<=1)

=> ∑ (xi - mean)² = 16*7

=> ∑ (xi - mean)² = 112

=> {(2-8)² +(4-8)² + (10-8)² + (12-8)² + (14-8)² + (x-8)² + (y-8)² } = 112

=> {(-6)² +(-4)² + (2)² + (4)² + (6)² + x² + 64 - 16x + y² + 64 -16y } = 112

=> {36 + 16 + 4 + 16 + 36 + x² + y² + 64 + 64 -16(x+y) } = 112

=> {108 + x² + y² + 128 -(16*14)} = 112        (since x+y =14)

=> {108 + x² + y² + 128 -224} = 112

=> x² + y² + 236 - 224 = 112

=> x² + y² + 12 = 112

=> x² + y² = 12-12

=> x² + y² = 100................2

Squaring equation 1, we get

(x+y)² = 196

=> x² + y² + 2xy = 196

=> 100 + 2xy = 196

=> 2xy = 196-100

=>2xy = 96

=> xy = 96/2

=> xy = 48.............3

Now (x-y)² = x² + y² - 2xy

                  = 100 - 2*48

                  = 100-96

                  = 4

=> x-y = √2

=> x-y = 2, -2

case 1: when x-y = 2 and x+y = 14

After solving it, we get x = 8, y= 6

case 2: when x-y = -2 and x+y = 14

After solving it, we get x = 6, y= 8

So the two numbers are 6 and 8