In a class test, the sum of Kamal's marks in Mathematics and English is 40.

Let the marks of Kamal in mathematics and english be $x$ and $y$, respectively.

According to the question:

$x+y=40 \quad \ldots$ (i)

Also,

$(x+3)(y-4)=360$

$\Rightarrow(x+3)(40-x-4)=360 \quad[$ From (i) $]$

$\Rightarrow(x+3)(36-x)=360$

$\Rightarrow 36 x-x^{2}+108-3 x=360$

$\Rightarrow 33 x-x^{2}-252=0$

$\Rightarrow-x^{2}+33 x-252=0$

$\Rightarrow x^{2}-33 x+252=0$

$\Rightarrow x^{2}-(21+12) x+252=0$

$\Rightarrow x^{2}-21 x-12 x+252=0$

$\Rightarrow x(x-21)-12(x-21)=0$

$\Rightarrow(x-21)(x-12)=0$

$\Rightarrow x=21$ or $x=12$

If $x=21$

$y=40-21=19$

Thus, Kamal scored 21 and 19 marks in mathematics and english, respectively.

If $x=12$

$y=40-12=28$

Thus, Kamal scored 12 and 28 marks in mathematics and english, respectively.