There are 2 ways your request can be interpreted, so I will attempt both:

1. Write the exact same letter but without "e", creating misspelled words
2. Write a recommendation letter without "e". Unfortunately this isn't 100% possible without some spelling mistakes, because there is no way to tell the professor I want a "recommendation" letter without using the word "recommend". But I will try my best to produce something comprehensible

It's not possible to write a grammatically correct letter without the letter "e", because most words have the letter including "Dear", "recommendation", and "letter"

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Subjct: Rqust for a Rcommndation Lttr

Dar Profssor [Profssor's Nam],

I hop this mail finds you wll. I am writing to rqust a rcommndation lttr from you for my graduat school application. I hav gratly njoyd your computr scinc cours this smstr, and I bliv that your lttr would b a valuabl addition to my application.

I hav bn imprssd with your taching styl and th way you hav mad complx concpts asy to undrstand. Your passion for computr scinc has inspird m to pursu a carr in this fild, and I am gratful for th knowldg and skills I hav gaind in your class.

I would b honord if you could writ a rcommndation lttr for m. I undrstand that you may hav a busy schdul, so plas lt m know if thr is any additional information or matrials that I can provid to mak th procss asir for you.

Thank you for your tim and considration. I look forward to haring from you soon.

Sincrly,
[Your Nam]

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Urg_nt, Brok_n K_yboard, R_qu_st for a R_commndation L_tt_r

D_ar Prof. [Prof_ssor's Nam_],

Firstly, I would lik_ to apologiz_ for th_ strang_ subj_ct and t_xt. You s__, my k_yboard is brok_n and I can't typ_ on_ of th_ l_tt_rs, you can probably gu_ss which on_ b_caus_ I'v_ r_plac_d all occurr_nc_s of it with "_". I assur_ you this is not a prank, and am only s_nding you this _mail b_caus_ it is absolut_ly urg_nt and I don't hav_ tim_ to fix.

I am writing to r_qu_st a r_comm_ndation l_tt_r from you for my graduat_ school application. I hav_ gr_atly _njoy_d your comput_r sci_nc_ cours_ this s_m_st_r, and I b_li_v_ that your l_tt_r would b_ a valuabl_ addition to my application.

Th_ d_adlin_ is du_ soon, so I would lik_ this l_tt_r as soon as possibl_. I am w_ll awar_ that I should hav_ s_nt this l_tt_r _arli_r, to giv_ you mor_ tim_ and so that I wouldn't hav_ to typ_ with a brok_n k_yboard as you s__ h_r_. Again, I am v_ry sorry for th_ strang_ wording, and also th_ lat_ notic_. How_v_r, I hav_ b__n so impr_ss_d with your class and don_ so w_ll that I hop_ you can ov_rlook th_s_ transgr_ssions.

I hav_ b__n impr_ss_d with your t_aching styl_ and th_ way you hav_ mad_ compl_x conc_pts _asy to und_rstand. Your passion for comput_r sci_nc_ has inspir_d m_ to pursu_ a car__r in this fi_ld, and I am grat_ful for th_ knowl_dg_ and skills I hav_ gain_d in your class.

I would b_ honor_d if you could writ_ a r_comm_ndation l_tt_r for m_. D_spit_ th_ lat_ notic_ I und_rstand that you may hav_ a busy sch_dul_, so pl_as_ l_t m_ know if th_r_ is any additional information or mat_rials that I can provid_ to mak_ th_ proc_ss _asi_r for you ASAP.

Thank you for your tim_ and consid_ration. I look forward to h_aring from you soon.

Sinc_r_ly,
[Your Nam_]
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