Why does ego take an upper hand in our mind after we complete a tough task?

It is because the ego wants to take the accolade, it likes to be appreciated and recognised. Moreover, the ego loves to dwell in self-importance and control.

Although ego is not able to do anything, yet it believes to be the ‘doer’ of every positive task that happens, and accordingly takes on the praise associated with the job. One takes credit for things that turn out good, but blames others or one’s own bad luck when things do not turn out as planned.

“Ego will always conduct itself to make sure that it does not appear bad”, says Param Pujya Dada Bhagwan, the founder of the movement of Akram Vignan.

In reality, only when numerous circumstances come together, can an event take place. However, one claims with egoism, "I did it." This is what the ego keeps doing throughout the life because it has taken on the identity of something it is not!
Let us examine the workings of our inner and outer actions.

The outer action happens through our body i.e. the physical part that we see. However, the inner action which is going on inside us has four parts – the mind, intellect, ego, and chitt (consciousness). Only after the decision is made in the inner part, does an outer action happen.

-The mind shows the thought.

-Through chitt, we can see the place, things, people etc. that come in our mind.

-The intellect takes a decision based on the knowledge it has in store.

-The ego finally, like a President, signs and endorses the final decision.

Thereafter, the outer action takes place when all the circumstances come together, which is in control of Nature. Thus, the ego’s only function actually is, that of endorsing the decision made by the intellect; it does nothing else. Yet the ego does the egoism of being the ‘doer’.

What is the Ego and how did it come into existence?
Param Pujya Dada Bhagwan explains that from a scientific perspective, when two different elements have come together, the ego came into being, as a natural occurrence.
Ego means the false ‘I’. All living beings are aware of their existence - “I am”. However, they do not know who they are - “What I am”. Therefore, we mistakenly believe the body or name given to us as our self. For example, one would say, ‘I am John/Sarah,' but that is a name given to identify the body. You are really not 'John/Sarah' and yet you believe so.

To say that which you are not, in reality, is called egoism, “I am this body, I am an accountant, I am her husband, I am his wife, I am of this age, I am fat, etc.” are all forms of egoism.

The ONLY way of removing this egoism of ‘I am the doer’ is, by attaining Self-realisation through the grace of an Enlightened One i.e. One without any ego. With the knowledge of the Self, your egoism dissipates and the correct knowledge of the Self sets in.

In Akram Vignan, through the ceremony of Self-realisation, three things happen: -The Soul and the body are separated.
-You understand the science of who am I and who is the doer, and thus, you are freed from all doership. -The correct understanding begins to prevail in worldly interactions.

Once you have acquired the correct knowledge of the real Self, the interference of the ego starts to lessen through the vision of the Self. The ego which has been bothering and controlling us so far, will gradually weaken and the strength of the Self will present itself in every aspect of our life.

Through this right vision, even if the ego takes an upper hand on completion of a tough task, you, as a Pure Soul, will now have the awareness that, ‘I am really a Pure Soul, the function of which is to only know and see every task as it happens and gets completed.’ With this awareness, the ego will gradually begin to dissolve and we will be able to experience the bliss of the Soul.

To know more: https://www.dadabhagwan.org/path-to-happiness/spiritual-science/what-is-ego-egoism/difference-between-ego-and-egoism/